{ "cells": [ { "cell_type": "markdown", "metadata": { "id": "yz_tXygF5gts" }, "source": [ "Modelación Numérica con Aplicación en Ingeniería Hidráulica y Ambiental\n", "------------\n", "CI6106-1 - Primavera 2022\n", "\n", "------------------\n", "Profesores: Yarko Niño - Luis Zamorano\n", "\n", "Profesor auxiliar: Aldo Muñoz\n", "\n", "Ayudante: Daniela Muñoz" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "id": "xdhXAw595JZR" }, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import matplotlib.animation as animation\n", "from IPython.display import HTML\n", "from tempfile import NamedTemporaryFile\n", "import timeit\n", "import time" ] }, { "cell_type": "markdown", "metadata": { "id": "LlMrN_yJopHp" }, "source": [ "# INTRODUCCION A SMOOTHED-PARTICLE HYDRODYNAMICS (SPH)\n", "\n", "El siguiente documento tiene por objetivo introducir ya en la práctica el método de SPH que hemos visto en clases.\n", "\n", "Veamos entonces la función Kernel y su implementación." ] }, { "cell_type": "markdown", "metadata": { "id": "NB3Qc8Y75xum" }, "source": [ "## Kernels\n", "Recordar que el Kernel es aquella función que usaremos para representar el \"Delta de Dirac\". En general tiene dos argumentos, la distancia vectorial ($\\vec{r}$) entre el punto (o partícula) en donde conocemos el valor de la función y el punto (párticula) donde nos interesa evaluar el valor de la función. En la práctica, buscamos siempre evaluar en particulas discretas a la que deseamos estimar el valor de una de las variables dependientes. El segundo argumento es el \"Smooth Length\". Este valor para efectos prácticos de todos estos ejercicios lo supondremos constante, pero puede perfectamente ser variable para cada partícula, de hecho suponerlo variable es una forma de trabajar la discontinuidad de partículas, como veremos más adelante.\n", "Presentaremos sólo algunos Kernel: \n", "### Kernel Spline cúbico\n", "\n", "Cubic Spline Kernel: [Monaghan1992]\n", "\\begin{equation}\n", "W(q) = \\left\\{ \n", " \\begin{array}{ c }\n", " \\sigma \\left[ 1- \\frac{3}{2} q^2 \\left( 1 - \\frac{q}{2} \\right) \\right] & \\quad \\textrm{si } 0 \\geq q \\geq 1 \\\\\n", " \\frac{\\sigma}{4} \\left( 2 - q \\right)^3 & \\quad \\textrm{si } 1 > q \\geq 2 \\\\\n", " 0 & \\quad q > 2\n", " \\end{array}\n", "\\right.\n", "\\end{equation}\n", "\n", "$\\sigma$ es un parámetro que depende del la dimensión del kernel. Asi dependiendo de la dimensión se define esta constante:\n", "\n", "\\begin{equation*}\n", "1 \\textrm{D} : \\sigma = \\frac{2}{3 h^1}\n", "\\end{equation*}\n", "\n", "\\begin{equation*}\n", "2 \\textrm{D} : \\sigma = \\frac{10}{7 \\pi h^2}\n", "\\end{equation*}\n", "\n", "\\begin{equation*}\n", "3 \\textrm{D} : \\sigma = \\frac{1}{\\pi h^3}\n", "\\end{equation*}\n", "\n", "Otro Kernel moderno \n", "### WendlandQuintic C2: para 2D y 3D.\n", "\n", "\\begin{equation}\n", "W(q)= \\left\\{\n", " \\begin{array}{ c 1 }\n", " \\alpha_d \\left( 1−\\frac{q}{2} \\right)^4 (2q+1) & \\textrm{si } 0 \\geq q \\geq 2 \\\\\n", " 0 & \\quad q > 2 \\\\\n", " \\end{array}\n", " \\right.\n", "\\end{equation}\n", "con $\\alpha_d$ una constante que depende de la dimensión:\n", "\\begin{equation*}\n", "\\alpha_d= \\frac{7}{4 \\pi h^2} \\textrm{para } \\text{dim}=2\n", "\\end{equation*}\n", "\n", "\\begin{equation*}\n", "\\alpha_d = \\frac{21}{16 \\pi h^3} , \\textrm{para } \\text{dim}=3\n", "\\end{equation*}\n", "\n", "\n", "### WendlandQuintic C2: para 1D.\n", "\n", "\\begin{equation}\n", "W(q)= \\left\\{\n", " \\begin{array}{ c 1 }\n", " \\alpha_d \\left( 1−\\frac{q}{2} \\right)^3 (1.5q+1) & \\textrm{si } 0 \\geq q \\geq 2 \\\\\n", " 0 & \\quad q > 2 \\\\\n", " \\end{array}\n", " \\right.\n", "\\end{equation}\n", "\n", "\\begin{equation*}\n", "\\alpha_d = \\frac{5}{8 h^1} \n", "\\end{equation*}\n", "\n", "Notar que la idea de la constante dimensional es hacerlo consistente con a propiedad de que su integral en todo el dominio es la unidad. Comó código, lo podemos definir como una función. " ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "id": "zx-u8vxl52Im" }, "outputs": [], "source": [ "def cubic(r, h, orden):\n", " \"\"\" r = distancia euclediana \n", " h = radio de busqueda\n", " orden = dimensiones (1,2,3)\n", " \"\"\" \n", " q = np.abs(r)/h\n", " res = np.zeros_like(q)\n", " if orden == 1:\n", " sigma = 2.0 / (h*3.0)\n", " elif orden == 2:\n", " sigma = 10/7/np.pi/h**2\n", " elif order == 3:\n", " sigma = 1/np.pi/h**3\n", " else:\n", " return \"error, valores validos:1,2,3\"\n", " \n", " res[q<=1] = sigma * (1.0 - (1.5 * q[q<=1]**2) + (0.75 * q[q<=1]**3))\n", " res[(q>1) & (q<=2)] = sigma * 0.25 * ((2.0 - q[(q>1) & (q<=2)]) ** 3.0)\n", " return res" ] }, { "cell_type": "markdown", "metadata": { "id": "k5ypQOACJMMJ" }, "source": [ "El otro Kernel quedan de tarea." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "id": "aZUrfjF_JSzR" }, "outputs": [], "source": [ "def WendlandQuintic_C2(r,h,orden):\n", " pass\n", " return 0" ] }, { "cell_type": "markdown", "metadata": { "id": "49moVXltqXHT" }, "source": [ "### Propiedades" ] }, { "cell_type": "markdown", "metadata": { "id": "tVF2j-89Hegy" }, "source": [ "Ahora que lo tenemos como función, podemos verificar que se cumple la condición mencionada. Siendo un medio discreto, podemos integrarlo sumando los términos y verifiquemos si la función implementada tiene un valor unitario (ó cercano). Veamos para el caso 1D:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "qazbmIFlt0bN", "outputId": "a1de6808-1196-4e0f-ca4d-9542921ba7b0" }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "La suma bajo la curva es: 0.999999\n" ] } ], "source": [ "r = np.linspace(-2,2,100)\n", "aa = cubic(r,0.5,1)*(r[1]-r[0])\n", "print(f\"La suma bajo la curva es: {np.round(aa.sum(),6)}\")" ] }, { "cell_type": "markdown", "metadata": { "id": "D5ZbdKQcH30K" }, "source": [ "Y podemos verificar también su forma, la cual asemeja una campana de Gauss pero mediante dos polinomios (uno para q = [0,1] y otro para el rango q = ]1,2])." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 282 }, "id": "bXwYFTZjt7ZM", "outputId": "510843bf-1296-46d3-a01e-bfbe758b0d72" }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(r,aa)" ] }, { "cell_type": "markdown", "metadata": { "id": "4eVuw_nKIO2D" }, "source": [ "Notemos que el radio de influencia ó mejor dicho, el dominio donde la función da soporte esta relacionada con el valor de h=1." ] }, { "cell_type": "markdown", "metadata": { "id": "Z5VecvJDq6wP" }, "source": [ "### Ejemplo de aplicación de la función Kernel." ] }, { "cell_type": "markdown", "metadata": { "id": "ZUzwCXfggeyn" }, "source": [ "Dada entonces esta función Kernel, usemosla para aplicar el método de aproximación de una función dado por el método de SPH.\n", "\n", "Por ejemplo interpolemos la función Seno usando SPH.\n", "\n", "\\begin{equation}\n", "f(x) = \\sin (x)\n", "\\end{equation}\n", "\n", "Esta ecuación la podemos representar considerando lo siguiente.\n", "\\begin{equation}\n", "f(x) = \\int_{\\Omega} f(x^\\prime)\\delta(x-x^\\prime) dx\n", "\\end{equation}\n", "\n", "En donde $\\delta$ es la función de Delta de Dirac. La cual puede ser remplazada por la función kernel $W$, de modo que:\n", "\n", "\\begin{equation}\n", "f(x) = \\int_{\\Omega_s} f(x^\\prime) W(\\left|x-x^\\prime \\right|, h) dx^\\prime + O(x^2)\n", "\\end{equation}\n", "\n", "Donde $\\Omega_s$ es una parte reducida del dominio en donde la función kernel da soporte. Esto tiene relación, como veremos, con el valor de h. Podemos ver esto mejor, realizando un simple ejercicio, en base a un función cualquiera. Veamos numericamente entonces que pasa con la función seno. Para ello veamos el dominio $\\omega$ que va de 0 a 2$\\pi$, y discreticemos en 40 partes." ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "id": "_cpZdeWAkZKJ" }, "outputs": [], "source": [ "N = 40" ] }, { "cell_type": "markdown", "metadata": { "id": "hQfwl0Cuko_R" }, "source": [ "Para suponer una función continua vamos a hacer un muestreo 10 veces mas grande que nuestra discretización.\n" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "id": "DinobpYaknEp" }, "outputs": [], "source": [ "N1 = 10*N" ] }, { "cell_type": "markdown", "metadata": { "id": "BK55N9eNk1pZ" }, "source": [ "Establecemos entonces un arreglo de la variable independiente en el dominio, para el caso discreto y para el caso continuo." ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "id": "fq_xGtgvfVg7" }, "outputs": [], "source": [ "\n", "X = np.linspace(0,4*np.pi,N1) #caso discreto\n", "X_i = np.linspace(0,4*np.pi,N) # caso continuo" ] }, { "cell_type": "markdown", "metadata": { "id": "5GbwVuiRlLDW" }, "source": [ "Construimos dos funciones: Una representa la función en puntos discretos $x^\\prime$ y la otra representa los puntos que deseamos interpolar y comparar con el caso continuo de referencia." ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "id": "n840ZVqSlIjK" }, "outputs": [], "source": [ "f_i = np.sin(X_i)\n", "f_x = np.sin(X)" ] }, { "cell_type": "markdown", "metadata": { "id": "EFMqoIDhlkHr" }, "source": [ "Vamos a evaluar la función en aquellos puntos donde no tenemos información (suponiendo que no conocemos la función seno). La integral propuesta anteriormente sigue siendo continua, por lo que debemos escribirla en forma discreta usando una sumatoria.\n", "\\begin{equation}\n", "f(x) \\approx \\sum_{\\Omega_s} f(x^\\prime) W(\\left|x-x^\\prime \\right|, h) \\Delta x^\\prime\n", "\\end{equation}\n", "\n", "La sumatoria anterior la podemos escribir con la siguiente función." ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "id": "JWX4Bph8ljE2" }, "outputs": [], "source": [ "def aprox(f_i,x_i,x,h):\n", " dx = x_i[1]-x_i[0] #dx en este caso es constante, pero puede no serlo.\n", " f_new = []\n", " for xx in x: #loop para cada valor de x (aproximamos por un rectangulo de centro x y ancho dx)\n", " W_i = cubic(xx-x_i, h, 1)\n", " f_new.append(np.dot(W_i,f_i)*dx)\n", " return f_new" ] }, { "cell_type": "markdown", "metadata": { "id": "Xz3aBbrYv490" }, "source": [ "La aplicamos para estimar la función en seno, en aquellos puntos donde no la concemos." ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "id": "7hKN18UMqBEM" }, "outputs": [], "source": [ "ff = aprox(f_i,X_i,X,0.25)" ] }, { "cell_type": "markdown", "metadata": { "id": "tDKwFCNNwLRE" }, "source": [ "Comparamos el resultado con la función seno original." ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 265 }, "id": "Ii-XBhduwDCY", "outputId": "07cfc4a0-3ff9-4ab2-d218-91874ff771bc" }, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plt.figure()\n", "### Funcion sin\n", "plt.plot(X,f_x, label='real sin(x)')\n", "### Funcion interpolada con SPH\n", "plt.plot(X,ff, label='SPH sin(x)')\n", "plt.scatter(X_i,f_i,label = \"f_i\")\n", "\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "id": "KKEfkTXzMOAV" }, "source": [ "Como se puede ver se logra una buena repreentación de la función. (Probar con un N más chico, que pasa? )\n", "\n", "Un aspecto importante de mencionar es que vectorialmente $\\Delta x$ representa un diferencial de volumen (discreto de integración). \n", "En efecto, representa lo siguiente: \n", "\\begin{equation}\n", "f(\\vec{x}) = \\int_{\\Omega} f(\\vec{x}^\\prime) \\delta(\\vec{x}-\\vec{x}^\\prime) dv\n", "\\end{equation}\n", "\n", "pensando en un fluido, podemos pensar que una partícula representa una cantidad física, la masa por ejemplo $dm$ como una cantidad fija y la densidad como una cantidad variable en el espacio $\\rho_a$, podemos reemplazar: \n", "\n", "$$\\rho_a dv = dm $$\n", "\n", "\\begin{equation}\n", "f(\\vec{x}) = \\int_{\\Omega} \\frac{f(\\vec{x}^\\prime)}{\\rho_a} \\delta(\\vec{x}-\\vec{x}^\\prime) \\rho_a dm\n", "\\end{equation}\n", "\n", "lo que en la práctica da la siguiente discretización para partículas con masa conocida $j$ y densidad conocida pero variable $\\rho_i$, \n", "\n", "\\begin{equation}\n", "f_i(\\vec{x_i}) \\approx \\sum_j f_j \\frac{m_j}{\\rho_j} W^\\prime(x_i - x_j)\n", "\\end{equation}\n", "\n", "Esta discretización representa la base para el método. \n", "Por ahora para fines didácticos mantendremos el uso de $\\Delta x$ como la derivada espacial.\n" ] }, { "cell_type": "markdown", "metadata": { "id": "Xzo14eG6HE0I" }, "source": [ "## Derivadas.\n", "Veamos como es la derivada, para ello consideremos la siguente función, y derivemos a ambos lados\n", "\n", "$$ f_a = \\sum_b f_b W(x_a - x_b) \\Delta x $$\n", "\n", "Debido a que hay dos funciones $f_a$ y $W$, su derivada es:\n", "\n", "$$ \\nabla f_a = \\sum_b \\left[ \\nabla f_b \\cdot W(x_a - x_b) \\Delta x + f_b \\cdot \\nabla W(x_a - x_b)\\right] \\Delta x $$\n", "\n", "Notar que la derivadas de valores constantes son zero, $f_b$ es conocida, por lo tanto, $f_b = 0$, y entonces: \n", "\n", "$$ \\nabla f_a = \\sum_b \\left[0+ f_b \\nabla W(x_a - x_b) \\right] \\Delta x $$\n", "\n", "simplificando:\n", "\n", "$$f(x) =\\sum_b f_b \\nabla W(x_a - x_b) \\Delta x $$\n", "\n", "Es decir sólo debemos considerar la derivada del Kernel, lo que es un plus importante." ] }, { "cell_type": "markdown", "metadata": { "id": "-F9-9h-tAEfr" }, "source": [ "De este modo.\n", "\\begin{equation}\n", "\\left< \\nabla f^\\prime(x) \\right> = \\int_{\\Omega_s} f(x^\\prime) \\nabla W(\\left|x-x^\\prime \\right|, h) dx^\\prime \n", "\\end{equation} \n", "\n", "discretamente\n", "\n", "\\begin{equation}\n", "\\left< \\nabla f^\\prime(x) \\right> \\approx \\sum_{\\Omega_s} f(x^\\prime) \\nabla W(\\left|x-x^\\prime \\right|, h) dx^\\prime\n", "\\end{equation} \n" ] }, { "cell_type": "markdown", "metadata": { "id": "gJ9eVgqay9tO" }, "source": [ "Hay que considerar que la expresión anterior es una aproximación. Al hacer una expansión en serie de Taylor esta expresión tiene un error del orden 1. Por lo que es común que este sujeto a errores, y de hecho así ocurre, como se puede ver por el trabajo de varios autores, que por lo demás trabajaron para tener una mejor opción. Por ahora, usaremos por simplicidad esa expresión y veremos más adelante una propuesta de mejora." ] }, { "cell_type": "markdown", "metadata": { "id": "PNhGgSYU0Qj1" }, "source": [ "## Derivada del Kernel.\n", "El Kernel es una función conocida por lo tanto su derivada podemos obtenerla considerando lo aprendido en los cursos de cálculo. " ] }, { "cell_type": "markdown", "metadata": { "id": "8sWgB0ePFKQ5" }, "source": [ "Hay que estimar la derivada de la función Kernel, W.\n", "por lo tanto usando la regla de la cadena podemos escribir en 1D:\n", "\n", "\\begin{equation}\n", "\\frac{dW}{dx} = \\frac{dW}{dq} \\frac{dq}{dx}\n", "\\end{equation}" ] }, { "cell_type": "markdown", "metadata": { "id": "1M5kW7uGI5Cx" }, "source": [ "por simplicidad y con el fin de ayudar al uso de la libería simbólica de python, vamos a aplicarla para deducir la derivada de la función Kernel. \n", "La idea es que pueda aplicar esta herramienta para obtener cualquier derivada de otro kernel." ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "id": "TBQbq2KPwGiM" }, "outputs": [], "source": [ "import sympy as sp" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "id": "hvDJ1sEfri0j" }, "outputs": [], "source": [ "W,q,h = sp.symbols(\"W , q , h\")\n", "r,x,x_prime,sigma = sp.symbols(\"r, x,xprime,sigma\" , real=True)" ] }, { "cell_type": "markdown", "metadata": { "id": "df84YAVSKBJZ" }, "source": [ "para el rango q =< 1:" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "id": "uxzJC1wgHXYA" }, "outputs": [], "source": [ "q1 = sigma * (1.0 - (1.5 * q**2) + (0.75 * q**3))" ] }, { "cell_type": "markdown", "metadata": { "id": "5XLBnezoKMJx" }, "source": [ "para el rango q > 1 y q < 2\n", "\n" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "id": "2GOFk0LJKEYB" }, "outputs": [], "source": [ "q2 = sigma * 0.25 * ((2.0 - q) ** 3.0)" ] }, { "cell_type": "markdown", "metadata": { "id": "sLutbaFmKnxx" }, "source": [ "Estimando la derivada \n", "\\begin{equation*}\n", "\\frac{dW}{dq}\n", "\\end{equation*}" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "id": "4VD6q8HkK4e8" }, "outputs": [], "source": [ "dq1 = q1.diff(q,1)\n", "dq2 = q2.diff(q,1)" ] }, { "cell_type": "markdown", "metadata": { "id": "E8bECX73LD0i" }, "source": [ "podemos ver el resultado de la derivada estimada para la primera función" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 38 }, "id": "Y7bGJ_p2LIFa", "outputId": "968e71c1-11e1-48b0-c627-b738e5a0f7d1" }, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\sigma \\left(2.25 q^{2} - 3.0 q\\right)$" ], "text/plain": [ "sigma*(2.25*q**2 - 3.0*q)" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dq1" ] }, { "cell_type": "markdown", "metadata": { "id": "wDLa57q6LLIC" }, "source": [ "y de la segunda parte de la función." ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 39 }, "id": "h1A_czS3LMxP", "outputId": "7bb4833d-7239-4be4-eacf-6f44729b6e1c" }, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle - 3.0 \\sigma \\left(1 - 0.5 q\\right)^{2.0}$" ], "text/plain": [ "-3.0*sigma*(1 - 0.5*q)**2.0" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dq2" ] }, { "cell_type": "markdown", "metadata": { "id": "aGvHp241LW06" }, "source": [ "también se puede pedir en latex (por si se quiere adjuntan a un documento)" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "926befeWLbH5", "outputId": "783663a6-e717-4fab-edf0-0aac941352e2" }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\\sigma \\left(2.25 q^{2} - 3.0 q\\right)\n" ] } ], "source": [ "print(sp.latex(dq1))" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "lM37w3BhLenh", "outputId": "d25793d0-34f6-4e9e-a26f-92e98183380c" }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "- 3.0 \\sigma \\left(1 - 0.5 q\\right)^{2.0}\n" ] } ], "source": [ "print(sp.latex(dq2))" ] }, { "cell_type": "markdown", "metadata": { "id": "5T-v7mVsLh2y" }, "source": [ "Entonces, los resultados (1D) que llevamos son los siguientes:\n", "\n", "\\begin{equation*}\n", "\\frac{dW}{dq} = \\left\\{ \n", " \\begin{array}{ c }\n", " \\sigma \\left(2.25 q^{2} - 3.0 q \\right) & \\quad \\textrm{si } 0 \\geq q \\geq 1 \\\\\n", " - 3.0 \\sigma \\left(1 - 0.5 q\\right)^{2.0} & \\quad \\textrm{si } 1 > q \\geq 2 \\\\\n", " 0 & \\quad q > 2\n", " \\end{array}\n", "\\right.\n", "\\end{equation*}" ] }, { "cell_type": "markdown", "metadata": { "id": "qNxlhIGIMOpL" }, "source": [ "Falta considerar la última derivada que es:\n", "\n", "$$ \\frac{dq}{dx} = \\frac{dq}{dr}\\frac{dr}{dx} = \\left( \\frac{d(\\left|r \\right|/h)}{dr} \\right) \\left( \\frac{d(x-x^\\prime)}{dx} \\right) $$" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "id": "kLrX8ntLNVMW" }, "outputs": [], "source": [ "qq = sp.Abs(r)/h" ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 53 }, "id": "jENUqohEOw6I", "outputId": "8e41c704-6918-4797-ef2c-6505ae99fbaf" }, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\frac{\\operatorname{sign}{\\left(r \\right)}}{h}$" ], "text/plain": [ "sign(r)/h" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dqq = qq.diff(r,1)\n", "#print(sp.latex(dqq))\n", "dqq" ] }, { "cell_type": "markdown", "metadata": { "id": "Vb9QDn1ERQoO" }, "source": [ "Con lo cual se obtiene \n", "\\begin{equation}\n", "\\frac{dq}{dx} = \\frac{r}{\\left| r\\right| h} 1\n", "\\end{equation}\n", "\n", "finalmente.\n", "\\begin{equation*}\n", "\\frac{dW}{dx} = \\left\\{ \n", " \\begin{array}{ c }\n", " \\sigma \\frac{r}{\\left| r\\right| h} \\left(2.25 q^{2} - 3.0 q \\right) & \\quad \\textrm{si } 0 \\geq q \\geq 1 \\\\\n", " -3.0\\sigma \\frac{r}{\\left| r\\right| h} \\left(1.0 - 0.5 q \\right)^{2.0} & \\quad \\textrm{si } 1 > q \\geq 2 \\\\\n", " 0 & \\quad q > 2\n", " \\end{array}\n", "\\right.\n", "\\end{equation*}" ] }, { "cell_type": "markdown", "metadata": { "id": "kW05i3Rt1MGX" }, "source": [ "La implementamos entonces en python como una función." ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "id": "2U_2gW50S_6S" }, "outputs": [], "source": [ "def dcubic(r, h, orden):\n", " \"\"\" r = distancia euclediana \n", " h = radio de busqueda\n", " orden = dimensiones (1,2,3)\n", " \"\"\" \n", " q = np.abs(r)/h\n", " dq = q/(r+1e-9) #dq/dx\n", " res = np.zeros_like(q)\n", " if orden == 1:\n", " sigma = 2.0 / (h*3.0)\n", " elif orden == 2:\n", " sigma = 10/7/np.pi/h**2\n", " elif orden == 3:\n", " sigma = 1/np.pi/h**3\n", " else:\n", " return \"error, valores validos:1,2,3\"\n", " q_aux1 = q[q<=1]\n", " dq_aux1 = dq[q<=1]\n", " q_aux2 = q[(q>1) & (q<=2)]\n", " dq_aux2 = dq[(q>1) & (q<=2)]\n", " res[q<=1] = sigma * dq_aux1 * (2.25 * q_aux1**2 - 3.0*q_aux1)\n", " res[(q>1) & (q<=2)] = -3.0* sigma * dq_aux2 * (1 - 0.5*q_aux2)**2.0\n", " return res" ] }, { "cell_type": "markdown", "metadata": { "id": "Vy69Y-MuUaEl" }, "source": [ "grafiquemos la función kernel y su derivada para entender mejor la función." ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "c54CtfF2UhIu", "outputId": "b44790ad-228a-4028-80fe-0280cd3ecd32" }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "La suma de la curva bajo la curva es: 0.0\n" ] } ], "source": [ "r = np.linspace(-2,2,100)\n", "bb = cubic(r,1.0,1)*(r[1]-r[0])\n", "aa = dcubic(r,1.0,1)*(r[1]-r[0])\n", "print(f\"La suma de la curva bajo la curva es: {np.round(aa.sum(),4)}\")" ] }, { "cell_type": "markdown", "metadata": { "id": "GWV2AA1-VZyg" }, "source": [ "notar que en este caso el área bajo la curva de su derivada es 0, para entender mejor esto podemos ver ambas gráficas." ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 265 }, "id": "bm0XRFmMViXI", "outputId": "692fa52c-feb5-4716-f770-ce8bee2ffb1d" }, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plt.figure()\n", "### Funcion Kernel\n", "plt.plot(r,bb, label='W(q)')\n", "### Derivada de la Funcion Kernel\n", "plt.plot(r,aa, label='DW/dr')\n", "plt.grid()\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "id": "ZwCjKq7IMwHt" }, "source": [ "Del gráfico obtenemos dos características muy relevantes:\n", "\n", "\n", "* La función Kernel es simétrica\n", "* La derivada del Kernel es antisimétrica.\n", "Esta propiedad es usada en varias derivaciones.\n" ] }, { "cell_type": "markdown", "metadata": { "id": "8u6Qki1q1rWA" }, "source": [ "### Ejemplo de aplicación de la derivada mediante SPH." ] }, { "cell_type": "markdown", "metadata": { "id": "xf49nPbkWjJL" }, "source": [ "Apliquemos lo aprendido para estimar la derivada de nuestra función seno. Sabemos que \n", "$$ \\frac{f(x)}{dx} = cos(x)$$\n", "\n", "Entonces, veamos si esta aproximación se acerca a la función coseno.\n", "\n", "$$ \\frac{f(x)}{dx} \\approx = \\sum_{\\Omega_s} f(x^\\prime) \\nabla W(\\left|x-x^\\prime \\right|, h) dx^\\prime $$\n", "\n", "contruimos entonces nuestra función, usando las funciones que escribimos en python, la idea es iterar en cada punto para obtener la derivada. " ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "id": "tXazZhrYeRc3" }, "outputs": [], "source": [ "def daprox(f_i,x_i,x,h):\n", " dx = x_i[1]-x_i[0] #dx en este caso es constante, pero puede no serlo.\n", " df_new = []\n", " for xx in x: #loop para cada valor de x\n", " dW_i = dcubic(xx-x_i, h, 1)\n", " df_new.append(np.dot(dW_i,f_i)*dx)\n", " ## en los bordes puede que de nan, reemplazamos por 0.\n", " return np.nan_to_num(df_new)" ] }, { "cell_type": "markdown", "metadata": { "id": "VSd4sS9MfOPT" }, "source": [ "y la aplicamos entonces a nuestra función." ] }, { "cell_type": "code", "execution_count": 28, "metadata": { "id": "yj8GSoM7fRXb" }, "outputs": [], "source": [ "dff = daprox(f_i,X_i,X,0.25)" ] }, { "cell_type": "markdown", "metadata": { "id": "O5Iyq-Z02d-x" }, "source": [ "Y graficamos." ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 265 }, "id": "VCPi7glMffa0", "outputId": "216149b4-2794-4b1f-d67f-ad4a9a6931fb" }, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plt.figure()\n", "### Funcion sin\n", "plt.plot(X,np.cos(X), label='df/dx = cos(x)')\n", "### Funcion interpolada con SPH\n", "plt.plot(X,dff, label='df/dx por SPH h=0.25')\n", "plt.scatter(X_i,f_i,label = \"f_i\")\n", "\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "id": "NRHNqIzTiGzZ" }, "source": [ "Podemos ver que la solución de SPH no esta mal pero oscila en torno a la solución continua. Cabe mencionar que para los punto donde se conoce el valor de la función, o cercanos la oscilación aproxima con casi un nulo error.\n", "\n", "Este efecto oscilatorio depende por una parte de la resolución de $f_i$, y de h. Podemos ver el efecto de esta última variable en la solución considerando variarla.\n", "Cambiemos entonces los valores de h y comparemos." ] }, { "cell_type": "code", "execution_count": 30, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 265 }, "id": "NaxJSQIZiGBh", "outputId": "ce02ec7c-32ca-4100-bc10-396cc60bd1af" }, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dff1 = daprox(f_i,X_i,X,0.5)\n", "dff2 = daprox(f_i,X_i,X,0.75)\n", "dff3 = daprox(f_i,X_i,X,1.00)\n", "fig = plt.figure()\n", "### Funcion sin\n", "plt.plot(X,np.cos(X), label='df/dx = cos(x)', linestyle = 'dashed', linewidth = 3)\n", "### Funcion interpolada con SPH\n", "plt.plot(X,dff1, label='df/dx por SPH (h=0.50)')\n", "plt.plot(X,dff2, label='df/dx por SPH (h=0.75)')\n", "plt.plot(X,dff3, label='df/dx por SPH (h=1.00)')\n", "\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "id": "7j5jQvQCkX7E" }, "source": [ "Podemos ver como al cambiar el valor de la variable la oscilación desparece pero a costo de precisión. En efecto, existen varias publicaciones en donde se trata este problema y se proponen soluciones, para efectos prácticos, h se establece en función de la distancia entre particulas con información, como regla del dedo:\n", "\n", "\\begin{equation}\n", "h = [1 - 2] dr^\\prime \n", "\\end{equation}\n", "probemos con $h = 1.5 dx^\\prime$" ] }, { "cell_type": "code", "execution_count": 31, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 282 }, "id": "TihzG0kPkVML", "outputId": "9db49bba-60aa-4e87-8b2e-4d22c56702a7" }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 31, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dr = X_i[1]-X_i[0]\n", "h = dr*1.5\n", "dff4 = daprox(f_i,X_i,X,h)\n", "fig = plt.figure()\n", "\n", "plt.plot(X,np.cos(X), label='df/dx = cos(x)', linestyle = 'dashed', linewidth = 3)\n", "plt.plot(X,dff4, label='df/dx por SPH (h=1.5 \\cdot dr)')" ] }, { "cell_type": "markdown", "metadata": { "id": "KXVKN7tDFvAT" }, "source": [ "Si bien el ajuste mejoró, igual queda una leve oscilación, pero es claramente una mejora. (Pruebe Uds. distintos valores) \n", "\n", "En la práctica profesional, los modelos DualSphysics, y SPHera recomiendan valores de 1.2 a 1.4 dr, usualmente 1.3 es un buen punto de partida. \n", "Por otro lado, podemos ver que cerca de los bordes existe una mal ajuste. Lo anterior se debe a dos factores, el efecto del borde propiamente tal, y la baja densidad de puntos al no haber partículas suficientes al inicio y fin. \n", "\n", "Existen varias formas de lidiar con ese problema.\n", "\n", "Para ello vamos a agregar puntos en los extremos. Lo anterior supone conocer el comportamiento de la función en los bordes, lo que es similar a imponer una condición de borde. \n", "Supongamos varios casos. En el caso de una función periodica, podemos jugar con su simetría y antisimetría. Definimos entonces una nueva función para calcular la derivada, considerando tres condiciones:\n", "\n", "\n", "1. Gradiente 0: la función no cambia y es constante en los extremos.\n", "2. Espejo simetríco: Se impone una pendiente inversa a la que trae la función, dependiendo si el punto del borde es un punto de inflexión puede dar un buen resultado. \n", "3. Espejo antisimétrico, Idem a la anterior. Esto impone una pendiente similar a la que trae, dependera del caso cual es mejor. \n", "4. mantener la pendiente del ultimo punto (tarea)\n" ] }, { "cell_type": "code", "execution_count": 32, "metadata": { "id": "flwgw_EfFtme" }, "outputs": [], "source": [ "def daprox2(f_i,x_i,x,h,option=1,fulloutput=False, f0=0,fN=0):\n", " \"\"\" option = 0 fi = dado con f0 a la izq, y fN a la der.\n", " option = 1 fi = cte (grad 0)\n", " option = 2 reflejo\n", " option = 3 -reflejo \"\"\"\n", "\n", " x0 = x_i[0] #distancia inicial \n", " xN = x_i[-1] #distancia final\n", " dx = x_i[1]-x0 #dx en este caso es constante, pero puede no serlo.\n", " particulas_nuevas = int(np.ceil(h/dx))+1 # para agregar particulas\n", " x0_new = x0-particulas_nuevas*dx #distancia extendida a la izquierda\n", " xN_new = xN+particulas_nuevas*dx # distancia extendida a la derecha\n", " x_left = np.arange(x0_new,x0,dx)\n", " x_right = np.arange(xN+dx,xN_new+dx,dx)\n", " if option == 1:\n", " fi_left = np.ones_like(x_left) * f_i[0]\n", " fi_right = np.ones_like(x_right) * f_i[-1]\n", " elif option ==2:\n", " fi_left = np.flip(f_i[1:particulas_nuevas+1])\n", " fi_right = np.flip(f_i[len(f_i) - particulas_nuevas-1:-1])\n", " elif option ==3:\n", " fi_left = np.flip(f_i[1:particulas_nuevas+1]) * -1\n", " fi_right = np.flip(f_i[len(f_i) - particulas_nuevas-1:-1]) * -1\n", " else:\n", " fi_left = np.ones_like(x_left) * f0\n", " fi_right = np.ones_like(x_right) * fN\n", "\n", " x_i_new = np.concatenate((x_left,x_i,x_right))\n", " f_i_new = np.concatenate((fi_left,f_i,fi_right))\n", "\n", " df_new = []\n", " for xx in x: #loop para cada valor de x\n", " dW_i = dcubic(xx-x_i_new, h, 1)\n", " df_new.append(np.dot(dW_i,f_i_new)*dx) \n", " if fulloutput:\n", " return x_i_new,f_i_new,np.nan_to_num(df_new)\n", " else:\n", " return np.nan_to_num(df_new)" ] }, { "cell_type": "markdown", "metadata": { "id": "dNfIKM8G31EU" }, "source": [ "Probemos entonces con la función anterior considerar los tratamientos en la frontera." ] }, { "cell_type": "code", "execution_count": 33, "metadata": { "id": "JL6YK091KaBw" }, "outputs": [], "source": [ "dr = X_i[1]-X_i[0]\n", "h = dr*1.5\n", "xxi,ffi,dff_b = daprox2(f_i,X_i,X,h,option=1,fulloutput=True)\n" ] }, { "cell_type": "markdown", "metadata": { "id": "NyZ0dTNS3-E-" }, "source": [ "#### Tratamiento con valor constante. " ] }, { "cell_type": "code", "execution_count": 34, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 390 }, "id": "ARWGa5wcPtLU", "outputId": "f4dca69c-43e6-4184-b955-e6c9533fc754" }, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize=(8,6))\n", "plt.title('Condición de borde gradiente 0 (fi=cte)')\n", "plt.plot(xxi,ffi, label='fi', linestyle = 'dashed',color = 'black' ,linewidth = 1)\n", "plt.plot(X,np.cos(X), label='df/dx = cos(x)', linestyle = 'dashed', linewidth = 3)\n", "plt.plot(X,dff_b, label='df/dx por SPH (h=1.5 \\cdot dr)')\n", "plt.legend(loc='lower left')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "id": "NQf02d0MnlbB" }, "source": [ "Podemos ver que el comportamiento es similar al caso anterior, esto se debe básicamente a que el valor constante no es representativo de la función. Veamos lo que sucede al hacer un flejo simétrico del borde." ] }, { "cell_type": "code", "execution_count": 35, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 390 }, "id": "pQ1b9cAXf79W", "outputId": "c0b0c3e9-5fb1-4486-8d7a-b3096c7a2827" }, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "xxi,ffi,dff_b = daprox2(f_i,X_i,X,h,option=2,fulloutput=True)\n", "fig = plt.figure(figsize=(8,6))\n", "plt.title('Condición de borde simetría')\n", "plt.plot(xxi,ffi, label='fi', linestyle = 'dashed',color = 'black' ,linewidth = 1)\n", "plt.plot(X,np.cos(X), label='df/dx = cos(x)', linestyle = 'dashed', linewidth = 3)\n", "plt.plot(X,dff_b, label='df/dx por SPH (h=1.5 \\cdot dr)')\n", "plt.legend(loc='lower left')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "id": "c0_rzFnBQoIZ" }, "source": [ "La condición anterior empeora como es esperable pues la función se aleja de los valores de la función seno. De esta manera, resulta natural pensar que la mejor aproximación en este caso corresponde a una función que asemeje a la función, por lo que una reflexión con antisimetría es al parecer la mejor opción." ] }, { "cell_type": "code", "execution_count": 36, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 390 }, "id": "SITA72B1f0KE", "outputId": "ab44cbaf-fdab-40fe-a916-18bf5d89a89b" }, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "xxi,ffi,dff_b = daprox2(f_i,X_i,X,h,option=3,fulloutput=True)\n", "fig = plt.figure(figsize=(8,6))\n", "plt.title('Condición de borde anti-simetría')\n", "plt.plot(xxi,ffi, label='fi', linestyle = 'dashed',color = 'black' ,linewidth = 1)\n", "plt.plot(X,np.cos(X), label='df/dx = cos(x)', linestyle = 'dashed', linewidth = 3)\n", "plt.plot(X,dff_b, label='df/dx por SPH (h=1.5 \\cdot dr)')\n", "plt.legend(loc='lower left')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "id": "mtjlgqX08teP" }, "source": [ "Podemos ver entonces que la recomendación de literatura es buena y que el borde requiere de entender el comportamiento de la función (ojo no de su derivada)." ] }, { "cell_type": "markdown", "metadata": { "id": "KpBBeJ-VoNzH" }, "source": [ "Aplicamos el mismo encabezado para la función que usamos para interpolar la función (no la derivada),de modo de incluir un tratamiento para el borde, ya que lo usaremos más adelante. " ] }, { "cell_type": "code", "execution_count": 37, "metadata": { "id": "VFhY8grsWCR6" }, "outputs": [], "source": [ "def aprox(f_i,x_i,x,h,option=1,fulloutput=False, f0=0,fN=0):\n", " \"\"\" option = 0 fi = dado con f0 a la izq, y fN a la der.\n", " option = 1 fi = cte (grad 0)\n", " option = 2 reflejo\n", " option = 3 -reflejo \"\"\"\n", "\n", " x0 = x_i[0] #distancia inicial \n", " xN = x_i[-1] #distancia final\n", " dx = x_i[1]-x0 #dx en este caso es constante, pero puede no serlo.\n", " particulas_nuevas = int(np.ceil(h/dx))+1 # para agregar particulas\n", " x0_new = x0-particulas_nuevas*dx #distancia extendida a la izquierda\n", " xN_new = xN+particulas_nuevas*dx # distancia extendida a la derecha\n", " x_left = np.arange(x0_new,x0,dx)\n", " x_right = np.arange(xN+dx,xN_new+dx,dx)\n", " if option == 1:\n", " fi_left = np.ones_like(x_left) * f_i[0]\n", " fi_right = np.ones_like(x_right) * f_i[-1]\n", " elif option ==2:\n", " fi_left = np.flip(f_i[1:particulas_nuevas+1])\n", " fi_right = np.flip(f_i[len(f_i) - particulas_nuevas-1:-1])\n", " elif option ==3:\n", " fi_left = np.flip(f_i[1:particulas_nuevas+1]) * -1\n", " fi_right = np.flip(f_i[len(f_i) - particulas_nuevas-1:-1]) * -1\n", " else:\n", " fi_left = np.ones_like(x_left) * f0\n", " fi_right = np.ones_like(x_right) * fN\n", "\n", " x_i_new = np.concatenate((x_left,x_i,x_right))\n", " f_i_new = np.concatenate((fi_left,f_i,fi_right))\n", " f_new = []\n", " for xx in x: #loop para cada valor de x\n", " W_i = cubic(xx-x_i_new, h, 1)\n", " f_new.append(np.dot(W_i,f_i_new)*dx)\n", " return f_new" ] }, { "cell_type": "markdown", "metadata": { "id": "7SUyVbtH4WCF" }, "source": [ "## Ejemplo aplicado a una ecuación 1D.\n", "\n", "Para ver el método pongamoslo en práctica a un ejemplo simple. \n", "Todavía no vamos a advectar las partículas, y por lo tanto las vamos a suponer estáticas, lo que no quita que podamos discretizar el espacio. De este modo en 1D. y Dx= será igual a $dr$." ] }, { "cell_type": "markdown", "metadata": { "id": "i_QiloSXJFSz" }, "source": [ "\\begin{equation}\n", "f_a = \\int f(x) W(x − x_a) dx = \\sum f_b W(x_b − x_a) \\Delta x\n", "\\end{equation}\n" ] }, { "cell_type": "markdown", "metadata": { "id": "JUGC6efu88L-" }, "source": [ "Pongamos en práctica la aproximación de SPH a un caso simple.\n" ] }, { "cell_type": "markdown", "metadata": { "id": "VD-jH8KBWE-5" }, "source": [ "La siguiente ecuación se conoce como ecuación de Burger, \n", "\n", "$$ \\frac{\\partial u}{\\partial t}+c(u)\\frac{\\partial u}{\\partial x}=\\nu \\frac {\\partial ^{2}u}{\\partial x^{2}}$$\n", "\n" ] }, { "cell_type": "markdown", "metadata": { "id": "3-Ifn__4LKNJ" }, "source": [ "para simplificar aun más la ecuación, vamos a considerar que sólo hay advección. Esta ecuación además es de primer orden y lineal, por lo que es fácil de tratar.\n", "$$\\frac{du}{dt} = -c(u) \\frac{du}{dx} $$\n", "y para hacerlo más fácil,\n", "\n", "$$c(u) = c_0 $$\n", "\n", "La parte temporal, en lo que respecta al método SPH puede ser tratada de varias formas, similar al caso de diferenias finitas, volumenes finitos, elementos, etc. \n", "Lo usual es considerar al tiempo como una dimensión que sólo avanza y de forma discreta. Suponemos entonces el método más simple, el de Euler:\n", "\n", "$$ \\frac{du}{dt} => \\frac{u^{n+1} - u^{n}} {\\Delta t} $$\n", "\n", "reemplazando en la ecuación anterior:\n", "\n", "$$ u^{n+1} = u^n - c \\Delta t \\frac{du^n}{dx} $$\n", "\n", "y considerando lo aprendido:\n" ] }, { "cell_type": "markdown", "metadata": { "id": "8xbpb4ncNKG7" }, "source": [ "$$ u_a^{n} = \\sum \\frac{m_b}{\\rho_b} u_b^{n} W(x_b − x_a)$$\n", "\n", "$$ \\frac{du_a^{n}}{dx} = \\sum \\frac{m_b}{\\rho_b} u_b^{n} \\frac{dW(x_b − x_a)}{dr_{ab}}$$" ] }, { "cell_type": "markdown", "metadata": { "id": "aMwZ1-bFbPwl" }, "source": [ "$$\\Delta x = \\frac{m_b}{\\rho_b} $$\n", "\n", "$$ u^{n+1} = \\sum u_b^{n} W(x_b − x_a) \\Delta x - c \\Delta t \\sum u_b^{n} \\frac{dW(x_b − x_a)}{dr_{ab}} \\Delta x $$" ] }, { "cell_type": "code", "execution_count": 38, "metadata": { "id": "jfuXIv5QK515" }, "outputs": [], "source": [ "#Seteamos las condiciones del problema.\n", "dx = 0.5\n", "L = 100\n", "u0 = 1.0\n", "uN = 0.0001\n", "Tiempo = 20.0\n", "c = 1.0" ] }, { "cell_type": "markdown", "metadata": { "id": "zWKqYkGc6QZ9" }, "source": [ "Generamos las variables." ] }, { "cell_type": "code", "execution_count": 39, "metadata": { "id": "xwYhW95mNJcN" }, "outputs": [], "source": [ "x = np.arange(0,L,dx)\n", "u = np.ones_like(x)*uN\n", "Courant = 0.8\n", "dt = dx/c*Courant\n", "tiempo = np.arange(0,Tiempo,dt)" ] }, { "cell_type": "code", "execution_count": 40, "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "y2-cFPnMv6n1", "outputId": "2a73d7af-0b90-47cd-b712-c80e2677cee4" }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0.5\n" ] } ], "source": [ "print(x[1]-x[0])" ] }, { "cell_type": "markdown", "metadata": { "id": "II2VXY2b6WOc" }, "source": [ "Como condicion inicial vamos a inicializar la mitad de las variables con un valor." ] }, { "cell_type": "code", "execution_count": 41, "metadata": { "id": "2fdoYXHwPjpb" }, "outputs": [], "source": [ "N = len(x)\n", "med = int(N/2)\n", "u[0:med] = u0 " ] }, { "cell_type": "code", "execution_count": 42, "metadata": { "id": "JtSgySsjiTGl" }, "outputs": [], "source": [ "u[0]=u0\n", "u[-1]=uN" ] }, { "cell_type": "markdown", "metadata": { "id": "IR6R1tdn6fHF" }, "source": [ "Como ya hemos visto el \"smooth Kernel\" es fundamental para obtener un buen resultado, probemos con la siguiente aproximación." ] }, { "cell_type": "code", "execution_count": 43, "metadata": { "id": "2Wctcn0_QZ0f" }, "outputs": [], "source": [ "h = dx*2.0\n" ] }, { "cell_type": "markdown", "metadata": { "id": "qaCSVrJa6oG1" }, "source": [ "Los resultados los vamos a ir almacenando en cada instante, para ello creamos una lista de arreglos, y almacenamos el primer arreglo." ] }, { "cell_type": "code", "execution_count": 44, "metadata": { "id": "7SFpoqHwRZBs" }, "outputs": [], "source": [ "U = []\n", "U.append(u)\n", "#for t in tiempo:\n" ] }, { "cell_type": "markdown", "metadata": { "id": "7N9uCct-60J7" }, "source": [ "Hacemos una primera iteración con el fin de chequear que todo esta en orden. Comparamos el tiempo inicial, con el avance. (puede hacer click varias veces)." ] }, { "cell_type": "code", "execution_count": 45, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 334 }, "id": "_MKbpuF0S06K", "outputId": "842f9aa6-718d-4ede-cf28-f392912afa6f" }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ 0. 0.4 0.8 1.2 1.6 2. 2.4 2.8 3.2 3.6 4. 4.4 4.8 5.2\n", " 5.6 6. 6.4 6.8 7.2 7.6 8. 8.4 8.8 9.2 9.6 10. 10.4 10.8\n", " 11.2 11.6 12. 12.4 12.8 13.2 13.6 14. 14.4 14.8 15.2 15.6 16. 16.4\n", " 16.8 17.2 17.6 18. 18.4 18.8 19.2 19.6]\n" ] }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "du = daprox2(u,x,x,h,option=0,f0=u0,fN=uN)\n", "unew = aprox(u,x,x,h,option=0,f0=u0,fN=uN) - c*dt*du\n", "unew[0] = u0\n", "unew[-1] = uN\n", "U.append(unew)\n", "u = unew\n", "fig = plt.figure()\n", "print(tiempo)\n", "plt.plot(x,U[0], label='df/dx = cos(x)', linestyle = 'dashed', linewidth = 3)\n", "plt.plot(x,U[-1], label='df/dx por SPH (h=1.5 \\cdot dr)')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "id": "KrN8cKhx7Bat" }, "source": [ "Se puede ver algunas oscilaciones menores. Aceleremos el proceso al tiempo final, usando un blucle." ] }, { "cell_type": "code", "execution_count": 46, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 282 }, "id": "M4uLw2CZTQPA", "outputId": "d83a6200-bfd2-4d1f-9ed5-db9f9ebc3be8" }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "el tiempo de ejecución es 1.442124843597412 seg.\n" ] }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "inicio = time.time()\n", "for t in tiempo:\n", " du = daprox2(u,x,x,h,option=1,f0=u0,fN=uN)\n", " unew = aprox(u,x,x,h,option=1,f0=u0,fN=uN) - c*du*dt\n", " unew[0] = u0\n", " unew[-1] = uN\n", " U.append(unew)\n", " u = unew\n", "fin = time.time()\n", "print (f\"el tiempo de ejecución es {fin - inicio} seg.\")\n", "plt.plot(x,U[0], label='tiempo = 0', linestyle = 'dashed', linewidth = 1)\n", "plt.plot(x,U[-1], label='Tiempo final', color= 'black')\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "id": "OXEX6JfkO93j" }, "source": [ "Podemos comparar este resultado con el de otro método. Por ejemplo en diferencias finitas.\n", "\n", "$$ U_i^{n+1} = U_i^{n} - C_0 (U_i - U_{i-1}) $$\n", "\n", "con $C_0$:\n", "$$C_0 = c\\frac{\\Delta t}{\\Delta x}$$" ] }, { "cell_type": "code", "execution_count": 47, "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "rnja3gOiPDN8", "outputId": "379662c0-ccb9-4dbf-8f98-8e92160a3982" }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "el tiempo de ejecución es 0.0009236335754394531 seg.\n" ] } ], "source": [ "#creamos una variable para guardar los resultados:\n", "\n", "u_res = []\n", "u_res.append(U[0])\n", "un = U[0]\n", "u = np.zeros_like(un)\n", "steps = int(Tiempo/dt)\n", "tt = 0\n", "inicio = time.time()\n", "for i in range(0,steps):\n", " tt += dt\n", " #print(\"resolviendo t=\",tt, \"-\",i)\n", " ### explicito => Ux^n+1 = Ux^n - Co *Du \n", " C = c*dt/dx\n", " dU = un[1:]-un[:-1]\n", " u[1:] = un[1:] -C*dU \n", " u[0]= u0\n", " u[-1] = uN\n", " u_res.append(u)\n", " un = u\n", "fin = time.time()\n", "print (f\"el tiempo de ejecución es {fin - inicio} seg.\")" ] }, { "cell_type": "code", "execution_count": 48, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 265 }, "id": "ZFIdXmhSQ3vP", "outputId": "d9a24c45-fe33-4e02-93c1-6dd13bad100e" }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAiMAAAGdCAYAAADAAnMpAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjUuMywgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/NK7nSAAAACXBIWXMAAA9hAAAPYQGoP6dpAABTI0lEQVR4nO3deXhTZf428PskbdI9LZTuq+xIKVC2gohLFRVRRkcRGVlEdARewY6KIMKMjpbfKAyoCAMziOMG6iguCIgVUKGArILsS2mhe0v3PTnvH6GnTTeakubJcn+uKxenOSfJt0dsb55VkmVZBhEREZEgKtEFEBERkXNjGCEiIiKhGEaIiIhIKIYRIiIiEophhIiIiIRiGCEiIiKhGEaIiIhIKIYRIiIiEspFdAFtYTAYkJGRAW9vb0iSJLocIiIiagNZllFSUoKQkBCoVC23f9hFGMnIyEB4eLjoMoiIiKgd0tPTERYW1uJ5uwgj3t7eAIzfjI+Pj+BqiIiIqC2Ki4sRHh6u/B5viV2EkbquGR8fH4YRIiIiO3OtIRYcwEpERERCMYwQERGRUAwjREREJBTDCBEREQnFMEJERERCMYwQERGRUAwjREREJBTDCBEREQnFMEJERERCMYwQERGRUGaHkZ9++gljx45FSEgIJEnCxo0br/maHTt2YODAgdBqtejWrRvWrVvXjlKJiIjIEZkdRsrKyhAbG4sVK1a06foLFy5gzJgxuPXWW3H48GHMmTMHTzzxBLZu3Wp2sUREROR4zN4o7+6778bdd9/d5utXrVqF6OhoLFmyBADQu3dv/PLLL/jnP/+J0aNHm/vxFnPiRB5Gjz7dpmtlGZAkuY3v3NbrOupa866T23B53fd+rWsb3iNLXdv4vlvmWmvdd9F/FwC50U1o7e9x4/vV9mtF/T0293Pbdr05/78bDIarDz30egP0er1yLEmAWq2Gq6sG3t7e8PHxRkhICCIjI+Dh4dns+6lUQOfOQGAg0KsXEBcHaLVt/R6J7FeH79qbkpKChIQEk+dGjx6NOXPmtPiaqqoqVFVVKV8XFxdbvK6Cgkqkpw+3+PsSETWWn2/887ffzHudVguMHAm8/DJw882Wr4vIVnT4ANasrCwEBgaaPBcYGIji4mJUVFQ0+5qkpCTodDrlER4e3tFlEhHZnKoq4IcfgFGjgD/8Abh8WXRFRB2jw1tG2mPevHlITExUvi4uLrZ4IImLC8KuXW37P9vYbCvx2jZeW9eE78jXth3vrfHapucqawzYdS4PsWE6+HtpIcttu1ftr6H1axv+t23rtZIkQa1Wt3q9Xm9AYWEhzp8/j19//RXbt2/HpUvpyvng4BAsXboUkZGRqK0F8vKAjAzg11+B7duBtDTjdRs3AqdOAXv2AD4+rZZHZHc6PIwEBQUhOzvb5Lns7Gz4+PjA3d292ddotVpoO7ij1M3NBcOHh3boZxBR626/pfmxE45FBaDT1ccg1NZOx4cffoiXXnoJGRkZyMwEZszYjq1btyI+frDJK/V6YN06YMECICsLOHECePRR4KuvALVawLdC1EE6vJsmPj4eycnJJs9t27YN8fHxHf3RRGTDKmv0+HhvGtILykWXYlUuLi6YMmUK9u3bh9jYWADAlStX8OCDD6KgoMDkWrUamDYN+PlnwM/P+NymTcBLL1m7aqKOZXYYKS0txeHDh3H48GEAxqm7hw8fRtrVtsR58+Zh0qRJyvV//vOfcf78ebzwwgs4efIk3n33XXz66ad49tlnLfMdEJFdqqjWY/6XR3E80/ID1O1BaGgofvrpJ4wYMQIAkJ6ejmnTpjWZAQUA3boBn39e3xryxhtAenqTy4jsltlhZP/+/RgwYAAGDBgAAEhMTMSAAQOwcOFCAEBmZqYSTAAgOjoamzZtwrZt2xAbG4slS5bg3//+t9BpvUQknurqOIvmfvk6Cx8fH2zYsAGdO3cGAGzcuBHvvvtus9fedhvw4ovGY4MBWL3aWlUSdTxJtoOfBMXFxdDpdCgqKoIPR24ROYSiihrE/u17vDtxIO6JCRZdjlDffPMN7rvvPgCAp6cnUlNT4e/v3+S6jAwgIsI4liQoCLh4EdBorF0tUdu19fc396YhIiFUVyeg2P4/hzre2LFj8cQTTwAwrnK9dOnSZq8LCQHGjTMeZ2UZZ9gQOQKGESISwlWtQvwNneHn6Sq6FJuwcOFCaK42c7z99tvIy8tr9roZM+qPW+jRIbI7DCNEJISbqxqfPDkMw7s27Y5wRuHh4UrrSGlpqbKFRmO33gr07Gk83rnTuPYIkb1jGCEiIWRZRkW1HrV6g+hSbMa8efNMWkcaT/UFjAvITZtW/3WjlROI7BLDCBEJUVVrQO+FW/D1kQzRpdiMsLAwk7EjGzZsaPa6W26pP9692wqFEXUwhhEiEqJ+aq/gQmzMU089pRx/8MEHzV4TGwu4uRmPU1KsURVRx2IYISIh6mbTGJhGTPTr1w8xMTEAjLuenzt3rsk1Gg0w+OrK8efPG2fWENkzhhEiEoItIy177LHHlOMPP/yw2WuGD68/ZusI2TuGESISQmLLSIsmTJig7AT84YcfNrtKLcMIORKGESISQpIk7Jl3O+7vz92zGwsLC8Ntt90GADh79iz27t3b5Jphw+qPOYiV7B3DCBEJE6Rzg7tGLboMm/SnP/1JOf7f//7X5HxAgHEDPQDYvx+oqrJWZUSWxzBCRMLM/PggdpzKEV2GTbr33nuVrppt27Y1e01dV01VFXDokLUqI7I8hhEiEub737OQVlAuugyb5O/vj7i4OADAkSNHkNXMlJmG40bYVUP2jGGEiISRJImzaVpx5513Ksc//PBDk/N103sB4PffrVERUcdgGCEiYVQSZ9O05o477lCOv//++ybnu3atPz5/3hoVEXUMhhEiEkYlSTAwi7QoPj4enp6eAIxhpPEUX50O6NzZeNzM2mhEdoNhhIiESbyjBwZF+okuw2ZptVrccnUjmuzsbBw9erTJNXWtI5cucUYN2S+GESIS5omRNyA23Fd0GTat4biR1rpqZBlITbVSUUQWxjBCRML8eDIb53NLRZdh0641iPWGG+qP2VVD9ophhIiESfz0CL4/ni26DJvWs2dPBAYGAgD27t0Lg8Fgcr7hIFaGEbJXDCNEJIxxACtHsLZGkiQMGTIEAFBYWIgzZ86YnGfLCDkChhEiEkYCd+1ti6FDhyrHjfep4fRecgQMI0QkjHHRM6aRa2ktjISEAFqt8ZgtI2SvGEaISJjuAV7w89SILsPmDR48WNmnpnEYUamA6Gjj8fnzQKMhJUR2gWGEiIT55MlhmDg0UnQZNk+n06FXr14AjPvUVFRUmJyv66qprASa2cKGyOYxjBAR2YG6rpra2locarRFL2fUkL1jGCEiYRKW7sRbyWeufSG1Om6EM2rI3jGMEJEwlTV6VNdykENbcEYNOTKGESIShuuMtF1MTAzc3d0BtB5G2DJC9ohhhIiEkSRw1942cnFxQVxcHAAgNTUVBQUFyrmoqPrrGEbIHjGMEJEwKkmCDKaRturXr59yfOzYMeXY3R3o0sV4nJlp7aqIrh/DCBEJs2ZSHB4fES26DLsRExOjHB89etTk3NXta5CdzVVtyf4wjBCRMN0CvBHo4ya6DLvRljBSVQUUF1uzKqLrxzBCRMIs/+EMvv0tQ3QZdqNv377KcUthBDC2jhDZE4YRIhJm09EM7E+9IroMu6HT6RAREQHAOGak4b4+DCNkzxhGiEgY1dX9Vqjt6rpqiouLkZaWpjzPMEL2jGGEiISRuM6I2VoaN9IwjOTkWLMiouvHMEJEwqgkMIyYqaUwEhBQfw1bRsjeuIgugIic1wMDwxCi42wac7SlZYRhhOwNwwgRCTPtJq4xYq6ePXvCxcUFtbW1DCPkMNhNQ0TCHM8oxoW8MtFl2BWNRoNevXoBAE6ePInq6moA7KYh+8YwQkTCvLTxKFbuOCu6DLtT11VTW1uLU6dOAQA0GsDPz3ieYYTsDcMIEQkjgRvltUfDxc+OHz+uHDdcEp7InjCMEJEwKkniPirt0LNnT+X4zJkzynFdGCkrMz6I7AXDCBEJYwwjTCPm6tGjh3J8+vRp5ZiDWMleMYwQkTC+Hq7w1HJSn7m6deumHLcURrjwGdkT/hQgImFWTxokugS75O7ujoiICKSlpeHUqVOQZRmSJHFGDdkttowQEdmhuq6awsJC5OfnA2A3DdkvhhEiEiZxw2Es/OqY6DLsUnPjRhhGyF4xjBCRMLmlVcgvrRZdhl1iGCFHwjBCRMKouGtvuzGMkCNhGCEiYSTu2ttuDCPkSBhGiEgYLnrWfpGRkXB1dQVQH0bc3QFvb+N5hhGyJ5zaS0TCJN7RAypJEl2GXXJxcUHXrl1x8uRJnDlzBgaDASqVCoGBQEkJ1xkh+8KWESISpm+oDn1CfESXYbfqloWvrKzEpUuXANR31RQWAlVVggojMhPDCBEJ89Xhy/ji4CXRZdit5saNdOlSfz4vz9oVEbVPu8LIihUrEBUVBTc3NwwdOhT79u1r9fply5ahZ8+ecHd3R3h4OJ599llUVla2q2Aichybj2bh6yMZosuwW82FET+/+vOFhVYuiKidzA4jGzZsQGJiIhYtWoSDBw8iNjYWo0ePRk4LHZQff/wxXnzxRSxatAgnTpzAf/7zH2zYsAHz58+/7uKJyL4ZZ9OIrsJ+de/eXTluLoxcuWLtiojax+wwsnTpUkyfPh1Tp05Fnz59sGrVKnh4eGDt2rXNXr97926MGDECjz76KKKionDnnXdiwoQJ12xNISLHx117r88NN9ygHF+4cAEAwwjZJ7PCSHV1NQ4cOICEhIT6N1CpkJCQgJSUlGZfM3z4cBw4cEAJH+fPn8d3332He+65p8XPqaqqQnFxscmDiBwP1xm5PiEhIdBoNADqw4ivb/15hhGyF2ZN7c3Ly4Ner0dgw5V1AAQGBuLkyZPNvubRRx9FXl4ebrrpJsiyjNraWvz5z39utZsmKSkJf/vb38wpjYjs0NDoTiit0osuw26p1WpERkbizJkzuHDhAmRZhp9f/VRpjhkhe9Hhs2l27NiB119/He+++y4OHjyIL774Aps2bcKrr77a4mvmzZuHoqIi5ZGent7RZRKRAI/FR+HpW7qKLsOuRUdHAwBKS0uRl5fHbhqyS2a1jPj7+0OtViO70dJ+2dnZCAoKavY1L7/8Mh577DE88cQTAICYmBiUlZXhySefxEsvvQSVqmke0mq10Gq15pRGRHYop6QSNXoZob7uokuxW3VhBDB21fj61s/tZRghe2FWy4hGo0FcXBySk5OV5wwGA5KTkxEfH9/sa8rLy5sEDrVaDQAcuEbk5BZvPok56w+JLsOuNR7Eyqm9ZI/MXg4+MTERkydPxqBBgzBkyBAsW7YMZWVlmDp1KgBg0qRJCA0NRVJSEgBg7NixWLp0KQYMGIChQ4fi7NmzePnllzF27FgllBCRc5IgcWrvdWrYMnL+/HmMGlV/ji0jZC/MDiPjx49Hbm4uFi5ciKysLPTv3x9btmxRBrWmpaWZtIQsWLAAkiRhwYIFuHz5Mrp06YKxY8fitddes9x3QUR2SSWxhfR6Ne2mqT/HMEL2QpLt4CdBcXExdDodioqK4OPDfSyIHMXcz3/DqewSbJw5QnQpdis/Px/+/v4AgISEBGzbtg3u7kBlJdC3L3D0qOACyam19fc396YhImFUKu7Ye706deqk/JBvvPAZx4yQvTC7m4aIyFKSHogRXYLdkyQJ0dHROHLkCC5evAi9Xg8/PzUyM9lNQ/aDLSNERHaubtxIbW0tLl26pIwbKSsDamrE1UXUVgwjRCTMv3ae49ReC2g8iJXTe8neMIwQkTAZhRU4lV0qugy719paI+yqIXvAMEJEwkjctdciGq81wum9ZG8YRohIGEkCmEWuX2vdNAwjZA8YRohIGJUkwcA0ct2ioqKUY44ZIXvEqb1EJMwfBoRiRLfOosuwex4eHggICEBOTg4uXrzIlhGyOwwjRCRM31AdAJ3oMhxCZGQkcnJykJGRAS+vWtT9eGcYIXvAbhoiEubAxQL878Al0WU4hIiICADGvX5qa3OV59lNQ/aAYYSIhPnhRA7e+vGM6DIcQl0YAYCKigzlmC0jZA8YRohIGJUEDmC1kIZhpKjoonLMMEL2gGGEiISRIMFgEF2FY2gYRq5cOd/gWEQ1ROZhGCEiYVQSuOiZhTQMI1lZZ6FWG485ZoTsAcMIEQkT3cUTw7pyaq8lNAwj6elpyvRetoyQPeDUXiIS5g8DwvCHAWGiy3AIXbp0gVarRVVVFdLS0uDrC+TlMYyQfWDLCBEJU1mjR1EF97i3BEmSlNYR48Jnxu6voiJwXA7ZPIYRIhJmzU/ncfuSHaLLcBh1YaS0tBTe3rUAjHv/FBeLrIro2hhGiEgYlUriRnkW1HDciItLmXLMrhqydQwjRCSMxHVGLKphGFGpipRjhhGydQwjRCSMcdde0VU4joZhxGDIV445vZdsHcMIEQkjgS0jltQwjFRXZynHbBkhW8epvUQkzOThURg/OFx0GQ6jYRgpK6vfn4YDWMnWMYwQkTBurmq4uapFl+EwwsPrg11R0WXlmGGEbB27aYhImG3Hs/HUB/tFl+Ew3N3d0aVLFwBAQUGq8jzDCNk6hhEiEubSlXLsOJUrugyHUtdVk5+fqjxXUiKoGKI2YhghImFUkgQOX7WsujAiy4XKc2wZIVvHMEJEwnDXXssLDQ29elSfQNgyQraOYYSIhJG4zojF1YeR+gTClhGydQwjRCTMoCg/LBjTW3QZDqW5lhGGEbJ1nNpLRML0CvJBryAf0WU4lLCwsKtHVVCp9DAY1OymIZvHlhEiEiYtvxxfHb7McSMWVN8yAri4lANgywjZPoYRIhJmz4V8zF5/mDv3WlDDMCJJpQA4gJVsH8MIEQmjkiQA3J/Gkjw9PaHT6QAAsmzcuZctI2TrGEaISBjp6p+cUWNZdeNGamoKAACVlUBNjciKiFrHMEJEwqiu/gSSufSZRdV11dS1jADsqiHbxjBCRML4eWjQL0zHMSMWxum9ZG84tZeIhLmlZwBu6RkgugyHw1VYyd6wZYSIyMHUrzXCVVjJPjCMEJEwm49mouv871BcydGVlsRuGrI3DCNEJJTeIHPMiIU1tz8Nu2nIljGMEJEwV5cZ4QqsFlbfTcOWEbIPDCNEJIykLHomuBAH4+/vD41GA4YRshcMI0QkTN2iZ2wZsSxJkhASEgJ205C9YBghImGGd/PHD4mjoHN3FV2KwzGOG2HLCNkHhhEiEsZL64JuAV5wUfNHkaUZx42wZYTsA38CEJEwJ7OK8ZdPj6CwvFp0KQ6HLSNkTxhGiEiYrKJK/O/gJZRX60WX4nAYRsieMIwQkTCqq7NpOHzV8oxhhN00ZB8YRohImLowYuDcXoszjhmpAVAJgC0jZNsYRohIGJWy6JnYOhxR41VY2TJCtoxhhIiECfPzwKxbu8HbjRuIW5pxnRGgbtwIW0bIljGMEJEwEZ098NzonvDz1IguxeFoNBp06dIFDCNkDxhGiEiYoooa7Dqbh/LqWtGlOKSGa43U1ABVVWLrIWoJwwgRCXMmuwQT/70XGYUVoktxSJzeS/aiXWFkxYoViIqKgpubG4YOHYp9+/a1en1hYSFmzpyJ4OBgaLVa9OjRA9999127CiYixyFxAGuH4vReshdmjxrbsGEDEhMTsWrVKgwdOhTLli3D6NGjcerUKQQEBDS5vrq6GnfccQcCAgLw+eefIzQ0FBcvXoSvr68l6iciO8ZdezsWW0bIXpgdRpYuXYrp06dj6tSpAIBVq1Zh06ZNWLt2LV588cUm169duxYFBQXYvXs3XF2Nm2FFRUVdX9VE5BCUdUbYNNIhjGNG8pWvGUbIVpnVTVNdXY0DBw4gISGh/g1UKiQkJCAlJaXZ13z99deIj4/HzJkzERgYiL59++L111+HXt/y8s9VVVUoLi42eRCR49G6qBDq6w6XugVHyKIat4ywm4ZslVlhJC8vD3q9HoGBgSbPBwYGIisrq9nXnD9/Hp9//jn0ej2+++47vPzyy1iyZAn+/ve/t/g5SUlJ0Ol0yiM8PNycMonITvQO9sGuF29D90Bv0aU4JHbTkL3o8Nk0BoMBAQEBWL16NeLi4jB+/Hi89NJLWLVqVYuvmTdvHoqKipRHenp6R5dJRORwGg9gZRghW2VWGPH394darUZ2drbJ89nZ2QgKCmr2NcHBwejRowfUarXyXO/evZGVlYXq6ua3DddqtfDx8TF5EJHjOZNdgsGv/YDfM4pEl+KQdDodtNr6n7PspiFbZVYY0Wg0iIuLQ3JysvKcwWBAcnIy4uPjm33NiBEjcPbsWRgMBuW506dPIzg4GBoNV10kcmZ6WUZuSRVq9BzA2hEkSYK/v1b5mi0jZKvM7qZJTEzEmjVr8P777+PEiRN4+umnUVZWpsyumTRpEubNm6dc//TTT6OgoACzZ8/G6dOnsWnTJrz++uuYOXOm5b4LIrJLnE3T8QID3ZXj/HwuwUq2yeypvePHj0dubi4WLlyIrKws9O/fH1u2bFEGtaalpUGlqs844eHh2Lp1K5599ln069cPoaGhmD17NubOnWu574KI7FLdHBqZYaTDhIR44+BB43FWVgUAbavXE4nQrq0yZ82ahVmzZjV7bseOHU2ei4+Px549e9rzUUTkwOoWPWMW6ThhYTrlOC+PLSNkm7g3DREJE+rrjk+fikePIE7t7ShRUZ2V4ytXagRWQtSydrWMEBFZgrtGjSHRnUSX4dCio7sox8XFhlauJBKHLSNEJMyVsmq8/t0JpOaViS7FYUVHhwAwTu8tK+NKt2SbGEaISJiSylqs/uk8MgorRJfisIwLn5UCACoq2BhOtolhhIiEuTp+lbv2diDjburG1c6qqri2E9kmhhEiEkal4jojHc3FxQUuLpUAAL3e/RpXE4nBMEJEwtSNYGAY6Vh1S8LLsgeqq1veMZ1IFIYRIhLGU+OCCUPCEazjv9g7krt7/SyaCxdyBFZC1DyGESISRufhiqQH+qEn1xnpUF5e9S1P588zjJDtYRghImFq9QacyCxGcSUX4+pIOl39j/oLF/IEVkLUPIYRIhKmqKIGdy//GXvO5YsuxaH5+bkqx+npBQIrIWoewwgRCSMpu/YKLsTB+fvXb4536VKxwEqImscwQkTCqJQFQZlGOlJAgIdynJVVKrASouYxjBCRMGwZsY7g4PoBwjk5XO2WbA/DCBEJo5IAN1cVuGNKxwoMrG8Zyc+vElgJUfO4UQERCePt5oqTr94tugyH5+1dH/euXKkVWAlR89gyQkTk4LwbLONSXi6hqoqtI2RbGEaISJiqWj3uWvYTfjyZLboUh+bl1fArb2RkZIgqhahZDCNEJNTJrBIUVXDRs47kbbLArRfDCNkchhEiEka6OnTVYLjGhXRd2DJCto5hhIiEqVtnhDN7O1bjlpHLly+LKoWoWQwjRCSMSllnhHGkI7FlhGwdp/YSkTCSBKycOBB9Q3WiS3Fonp4Nv+KYEbI9DCNEJIwkSbg7Jlh0GQ5PpQI8PWWUlUkAvNlNQzaH3TREJNSan87j94wi0WU4vPqFz9gyQraHYYSIhPq/LSdxKK1QdBkOr37cCMeMkO1hGCEioSQJkDmAtcPVz6jxQmlpKYqLi0WWQ2SCYYSIhJIkibv2WkF9y4grAC1bR8imMIwQkVASOLXXGrgKK9kyhhEiEuqOPoGI6ORx7QvpujRea4QzasiWcGovEQn1zqMDRZfgFNgyQraMLSNEJFRuSRXKqmpFl+HwuAor2TKGESIS6rYlO/Dhnouiy3B4bBkhW8YwQkRCqSSJG+VZAceMkC1jGCEioVQSZ9NYA1tGyJYxjBCRUCpJArNIxzMNI8YxI1xsjmwFwwgRCSVJgIGrnnU4024aL9TU1CAvL09UOUQmOLWXiIT66YVb4aLiv4s6WuOWEQDIyMhAly5dhNRD1BB/AhCRUB4aF2hc+KOoozVuGQHAcSNkM/gTgIiE+n+fHMJn+9NFl+HwmmsZ4YwashUMI0Qk1MGLV5BWUC66DIfHlhGyZQwjRCQcJ3V0vJbGjBDZAoYRIhJKpeI6I9bQXMsIu2nIVjCMEJFQXIHVOjQa48OILSNkWzi1l4iESryjByI6eYguwyl4eQEFBYBa7Qu9nmGEbAfDCBEJdX//UNElOA1vb2MYkSQfAEB2djZqa2vh4sJfBSQWu2mISKitv2fhcHqh6DKcQt24EVn2uPqnjKysLIEVERkxjBCRUG9uPYVvjrC7wBrqZtTo9W6o+/HPQaxkCxhGiEgolSRxNo2VmM6o8QTAMEK2gWGEiISSJK4zYi3NrTVy6dIlIbUQNcQwQkRCSZLEreythGuNkK1iGCEiofqG+CCcU3utgi0jZKs4n4uIhHrjoVjRJTgNtoyQrWLLCBEJpTfI0BvYTWMNDVtGPDyCADCMkG1gGCEioR54dxde+vKo6DKcQsOWET+/cADGbhqO2SHRGEaISCjjAFbRVTiHhi0jPj7GlW8rKytx5coVQRURGbUrjKxYsQJRUVFwc3PD0KFDsW/fvja9bv369ZAkCePGjWvPxxKRA1JJ3LXXWhq2jHh5BSnH7Koh0cwOIxs2bEBiYiIWLVqEgwcPIjY2FqNHj0ZOTk6rr0tNTcVzzz2HkSNHtrtYInI8xkXPRFfhHBq2jLi7ByjHnFFDopkdRpYuXYrp06dj6tSp6NOnD1atWgUPDw+sXbu2xdfo9XpMnDgRf/vb33DDDTdcV8FE5FiMi54xjVhDw5YRjaaTcsyWERLNrDBSXV2NAwcOICEhof4NVCokJCQgJSWlxde98sorCAgIwLRp09r0OVVVVSguLjZ5EJFjWvHoQCy4t4/oMpxCw5YRFxc/5ZgtIySaWWEkLy8Per0egYGBJs8HBga2uPPjL7/8gv/85z9Ys2ZNmz8nKSkJOp1OeYSHh5tTJhHZkQAfN3Ty1Iguwyk0bBmRpPpkwpYREq1DZ9OUlJTgsccew5o1a+Dv79/m182bNw9FRUXKIz09vQOrJCKR3vnxDN7bdUF0GU6hYcuILHsqxwwjJJpZK7D6+/tDrVYjOzvb5Pns7GwEBQU1uf7cuXNITU3F2LFjlecMBoPxg11ccOrUKXTt2rXJ67RaLbRarTmlEZGdSjmfD18PDaaOiBZdisNr2DJSVaWBRqNBdXU1u2lIOLNaRjQaDeLi4pCcnKw8ZzAYkJycjPj4+CbX9+rVC0ePHsXhw4eVx3333Ydbb70Vhw8fZvcLEUElSQDHr1qFh4dxwDAAlJZKCAkJAcCWERLP7L1pEhMTMXnyZAwaNAhDhgzBsmXLUFZWhqlTpwIAJk2ahNDQUCQlJcHNzQ19+/Y1eb2vry8ANHmeiJyTJElcZ8RKVCrA0xMoLQVKSoCwsDCkpqaioKAAFRUVcHd3F10iOSmzw8j48eORm5uLhQsXIisrC/3798eWLVuUQa1paWlQqbiwKxG1DRc9sy5vb2MYKS0FYmNDlecvX76Mbt26CayMnFm7du2dNWsWZs2a1ey5HTt2tPradevWtecjichB/WFAKNQqSXQZTqNu3EhJCRAayjBCtqFdYYSIyFLu7x967YvIYupm1JSWAqGhYcrzHMRKIrE/hYiEOnqpCEfSC0WX4TTqWkb0eiAwMEJ5nmGERGIYISKh3v7xDJYnnxFdhtNouNaIn199GOF6TiQSwwgRCaXibBqrarjWiE5X303DMEIiMYwQkVCSBO7aa0UNW0Y8PAKgVqsBMIyQWAwjRCSUSpK4a68VNWwZKS9XKzNqGEZIJIYRIhIqwEeLQB830WU4jYYtI6WlUFbCzsvLQ0VFhaCqyNlxai8RCbVo7I2iS3AqDVtGSkpgsi1Heno6evToIaAqcnZsGSEiciIttYwA7KohcRhGiEiol748isfX/Sq6DKdxrZYRIhEYRohIqIpqPUora0WX4TTYMkK2iGGEiITirr3WxZYRskUMI0QkFHfttS62jJAtYhghIqEkCWAUsZ7GLSNdunSBVqsFwDBC4nBqLxEJNevW7qiq1Ysuw2k0bhmRJAlhYWE4d+4cwwgJw5YRIhIqorMHugd6X/tCsojGLSMAEBFh3DCvuLgYxcXFAqoiZ8cwQkRCfftbBlbtPCe6DKfRMIyUlhr/5LgREo1hhIiE2nM+H18fzhBdhtPQaIwPoL5lhGGERGMYISKhVJLEAaxWVjduhC0jZCsYRohIKO7aa311XTVsGSFbwTBCRMJxnRHraq1lJC0tTUBF5Ow4tZeIhBp2Qyd08daKLsOp1LWMVFQAtbX1s2kAhhESg2GEiIS6q2+w6BKcTsO1RsrKAJ1OB19fXxQWFuLixYviCiOnxW4aIhIqo7ACJzK5toU1NbfWSGRkJABjy4hez0XoyLoYRohIqPdTUvH0hwdEl+FUGraM1IWRqKgoAEBtbS0yMjjVmqyLYYSIhJLAqb3WptPVHxcVGf+saxkBwK4asjqGESISirv2Wl9zYaSuZQQAUlNTrVoPEcMIEQmlkiQYDKKrcC4+PvXHdVvRNAwjbBkha2MYISKh3DVqeLtxYp81Xaubhi0jZG38CUBEQs28tRtm3tpNdBlOhd00ZGvYMkJE5GSaCyN+fn7wvjrNht00ZG0MI0Qk1Acpqfjjyt2iy3AqDcNI3ZgRSZKUrpqLFy/CwIE8ZEUMI0QkVFFFDVLzy0WX4VQaDmCtaxkB6rtqqqurkZ2dbd2iyKkxjBCRUBJ37bW65rppAA5iJXEYRohIKEkCFz2zspbCCAexkigMI0QklEqSuOiZlXl5AaqrP/2LG2wLxLVGSBRO7SUioe7uG4Q+wT7XvpAsRpKM40YKC9lNQ7aBYYSIhIrs7InIzp6iy3A6zYURdtOQKOymISKhDqVdwcod50SX4XTqxo00DCP+/v5wd3cHwG4asi6GESIS6mBaId7+8YzoMpxOXRipqjI+AOPMprrWkdTUVK41QlbDMEJEQnHXXjGaW/gMALp27QoAqKysRGZmppWrImfFMEJEQhln04iuwvm0NL23LowAwNmzZ61YETkzhhEiEkqSwEXPBGhpFdaGYeTcOY7lIetgGCEioaI6e2JMTLDoMpxOS9003brV76DMMELWwqm9RCTUzT264OYeXUSX4XTa0k3DMELWwpYRIhKqtKoW6QXcKM/aWlsSXnV1eVaOGSFrYRghIqG+PZKBkf/YznEjVtZSGNFoNAgPDwfAlhGyHoYRIhJKJUkAAGYR62o4gLXhmBGgftxIYWEhCgoKrFgVOSuGESIS6moW4VojVtZSywjA6b1kfQwjRCRUXcsI1xqxrraGEXbVkDUwjBCRUGwZEYNhhGwJp/YSkVDj+ofivtgQqFWS6FKcSlvGjADspiHrYBghIqFUKgkqMIhYW0srsALADTfcoByzZYSsgd00RCTU7rN5+OPK3aio1osuxam4uACensbjxmHE29sbAQEBABhGyDoYRohIqCvlNdh/8QpquV291dWNG2kcRoD6rprMzEyUlZVZsSpyRgwjRCRU/QBWsXU4o9bCCAexkjW1K4ysWLECUVFRcHNzw9ChQ7Fv374Wr12zZg1GjhwJPz8/+Pn5ISEhodXrici5KONWGUasrm7cSGkpoG/US9ajRw/l+PTp01asipyR2WFkw4YNSExMxKJFi3Dw4EHExsZi9OjRyMnJafb6HTt2YMKECdi+fTtSUlIQHh6OO++8E5cvX77u4onI/knKOiNMI9bWcHpvSYnpuV69einHJ0+etFJF5KzMDiNLly7F9OnTMXXqVPTp0werVq2Ch4cH1q5d2+z1H330EWbMmIH+/fujV69e+Pe//w2DwYDk5OTrLp6I7F/fUB3e+GM/uGvUoktxOq2tNdIwjJw4ccJKFZGzMiuMVFdX48CBA0hISKh/A5UKCQkJSElJadN7lJeXo6amBp06dWrxmqqqKhQXF5s8iMgxhfq646FB4XBzZRixttbCSPfu3ZXde9kyQh3NrDCSl5cHvV6PwMBAk+cDAwORlZXVpveYO3cuQkJCTAJNY0lJSdDpdMqjbgdJInI8lwsr8OGeiyivrhVditNpGEYa/5tPq9Uq642cPHkSBs52og5k1dk0ixcvxvr16/Hll1/Czc2txevmzZuHoqIi5ZGenm7FKonImk5nl2DBxmMoqWQYsbbWFj4D6rtqysvLOc6POpRZYcTf3x9qtRrZ2dkmz2dnZyMoKKjV17755ptYvHgxvv/+e/Tr16/Va7VaLXx8fEweROSY6ibTcACr9bXWTQNwECtZj1lhRKPRIC4uzmTwad1g1Pj4+BZf949//AOvvvoqtmzZgkGDBrW/WiJyONy1Vxxf3/rjwsKm5zmIlazF7L1pEhMTMXnyZAwaNAhDhgzBsmXLUFZWhqlTpwIAJk2ahNDQUCQlJQEA/u///g8LFy7Exx9/jKioKGVsiZeXF7y8vCz4rRCRPapb9Exmy4jVNZxHUFDQ9Hzv3r2VY7aMUEcyO4yMHz8eubm5WLhwIbKystC/f39s2bJFGdSalpamjMAGgJUrV6K6uhp//OMfTd5n0aJF+Otf/3p91ROR3fPz0GBEt87QqLkgtLX5+9cf5+U1Pd+zZ0/lmGGEOpIk28E/R4qLi6HT6VBUVMTxI0REFnLmDFC30OrEicCHHza9JiAgALm5uQgODkZGRoZ1CyS719bf3/ynCBEJpTfIKK+uhYGDRqzuWi0jQP24kczMTBQ1N8qVyAIYRohIqP2pBeizcCsu5HNnWGvT6QD11bXmWgojHDdC1mD2mBFbZTAYUF1dLboMojZxdXWFWs0VRwFAdXWnPNvvMHY8KhXQuTOQk3PtlhHAGEaGDh1qperImThEGKmursaFCxe4QiDZFV9fXwQFBSkbxTkrFWfTCOXv33oYadgycuzYMStVRc7G7sOILMvIzMyEWq1GeHi4yUweIlskyzLKy8uVna6Dg4MFVySWxHVGhKobN1JWBlRWAo0Xx264SOWRI0esWBk5E7sPI7W1tSgvL0dISAg8PDxEl0PUJu7u7gCAnJwcBAQEOHWXDVdgFatz5/rj/HwgNNT0fHBwMPz9/ZGXl8cwQh3G7psR9Ho9AOPqsET2pC4819TUCK5ErBtDdNg3/3Z0C+AiiCJca0aNJEmIjY0FYAzPbd0Ulcgcdh9G6jh7vzvZH/6dNdK4qBDg4wZXLnomRFum99aFEYBdNdQx+H8/EQmVXlCOJ/+7H6l5nNorAsMI2QKGERuyY8cOSJKEwuZ2rCJyUMWVNfj+eDaKKpy7u0oUhhGyBQwjgtxyyy2YM2eOyXPDhw9HZmYmdA339XYyn332GXr16gU3NzfExMTgu+++E10SdbC6XXs5fFWMtoSR3r17w9XVFQBw+PDhji+KnA7DiA3RaDROve7E7t27MWHCBEybNg2HDh3CuHHjMG7cOK5t4OBUytRexhER2hJGNBqNst7IqVOnUFlZaYXKyJkwjAgwZcoU7Ny5E8uXL4ckSZAkCampqc120/zyyy8YOXIk3N3dER4ejmeeeQZlZfV961FRUfj73/+OSZMmwcvLC5GRkfj666+Rm5uL+++/H15eXujXrx/279+vvGbdunXw9fXFxo0b0b17d7i5uWH06NFIT083qXPlypXo2rUrNBoNevbsiQ8++KBD78vy5ctx11134fnnn0fv3r3x6quvYuDAgXjnnXc69HNJrPpFz8TW4awaTu1tKYwA9V01er0ev//+ewdXRc6GYUSA5cuXIz4+HtOnT0dmZiYyMzMRHh7e5Lpz587hrrvuwoMPPojffvsNGzZswC+//IJZs2aZXPfPf/4TI0aMwKFDhzBmzBg89thjmDRpEv70pz/h4MGD6Nq1KyZNmmSywmV5eTlee+01/Pe//8WuXbtQWFiIRx55RDn/5ZdfYvbs2fjLX/6CY8eO4amnnsLUqVOxffv2Fr+vjz76CF5eXq0+fv755xZfn5KSgoSEBJPnRo8ejZSUlGveU7Jf/l5azLu7F0J93UWX4pQatozk57d8HceNUEey+0XPWpJTXImckiqT53Turgjv5IHKGj3O5pQ2eU3fUONYjXO5paio1pucC/Nzh6+HBvmlVcgsMm2i9NS6INrfs8216XQ6aDQaeHh4ICgoqMXrkpKSMHHiRGVsSffu3fHWW29h1KhRWLlyJdyuLpV4zz334KmnngIALFy4ECtXrsTgwYPx0EMPAQDmzp2L+Ph4ZGdnK59XU1ODd955R9ln4v3330fv3r2xb98+DBkyBG+++SamTJmCGTNmAAASExOxZ88evPnmm7j11lubrfe+++675r4VoY1XVGogKysLgYGBJs8FBgZyXQMH5+epwVOjuoouw2n5+AAuLkBtbdtaRgCGEbI8hw0jH+1Nw/LkMybPjesfgmWPDEBWUSXuffuXJq9JXTwGAPDcZ0dwKK3Q5Nw/x8fiDwPCsOloJhZ+ZdpEObK7Pz6YZvnNo44cOYLffvsNH330kfKcLMswGAy4cOGC0ofbcLnmul/mMTExTZ7LyclRwoiLiwsGDx6sXNOrVy/4+vrixIkTGDJkCE6cOIEnn3zSpJ4RI0Zg+fLlLdbr7e0Nb2/v9n675KTKqmrx0+lcDInuhM5eWtHlOB1JMraOZGW1PYwcPHjQCpWRM3HYMDJxaATu6GP6r2ydu3E0eJDODd/+v5tafO2bD8U22zICAGNigjEwws/knKe2Y25jaWkpnnrqKTzzzDNNzkVERCjHdaPcgfqFtJp7rqM3Evzoo4+UFpqWbN68GSNHjmz2XFBQELKzs02ea9iaQ44pr7QKT390EJ9MH4Z4hhEh2hJGunTpgqioKKSmpuLAgQOoqakx+TlDdD0cNowE+LghwMet2XNurmqlS6Y5Xbu0vCx1Zy+tRf71ptFolKXsWzJw4EAcP34c3bp1u+7Pa6y2thb79+/HkCFDABhHyBcWFiqtLb1798auXbswefJk5TW7du1Cnz59WnzP6+2miY+PR3JyssmU523btiE+Pr4t3xLZKWVqL0ewClM3bqSiAigvB1ra5mvYsGFITU1FRUUFjh49ioEDB1qvSHJoDhtGbF1UVBT27t2L1NRUeHl5oVOnTk2umTt3LoYNG4ZZs2bhiSeegKenJ44fP45t27Zd9wwTV1dX/L//9//w1ltvwcXFBbNmzcKwYcOUcPL888/j4YcfxoABA5CQkIBvvvkGX3zxBX744YcW3/N6u2lmz56NUaNGYcmSJRgzZgzWr1+P/fv3Y/Xq1e1+T7If3LVXnMbTexs0vJoYNmwY1q9fDwDYs2cPwwhZDGfTCPLcc89BrVajT58+6NKlC9LS0ppc069fP+zcuROnT5/GyJEjMWDAACxcuBAhISHX/fkeHh6YO3cuHn30UYwYMQJeXl7YsGGDcn7cuHFYvnw53nzzTdx4443417/+hffeew+33HLLdX92S4YPH46PP/4Yq1evRmxsLD7//HNs3LgRffv27bDPJPFUqrpFz5hGRGnr9N6GrZR79uzpwIrI2bBlRJAePXo0mbIaFRXVpKl68ODB+P7771t8n9TU1CbPNX6P5t4XAB544AE88MADLb73008/jaeffrrF8x3hoYceUmYBkXNwVUvoFeQND41adClOqy0LnwFA//79odVqUVVVxTBCFsWWESISKsDbDVvm3Iy4yKZdlWQdbQ0jGo1G6Zo5c+YM8lq7mMgMDCNERE6urQufAcZxI3X27t3bQRWRs2EYcUJTpkzhzsBkM3JLqtDr5c3YfjJHdClOq60tI4BpGGFXDVkKwwgRCSVJQGWNAbWcTiOMOWGEg1ipIzCMEJFQ3LVXvIZhJDe39WvDwsKUGX179+5FbW1tB1ZGzoJhhIiEurppLxc9E6jhIseNNu9uQpIk3HSTcQXrkpISkx3BidqLYYSIhKpfgVVwIU7Mza0+kFy8eO3rG+6uvW3btg6qipwJwwgRCeXl5oLNs0diRHf/a19MHSYy0vhnZiZQVdX6tXfccYdyzDBClsAwQkRCqVUSegf7wMeNm66JVBdGAKCZBaFNREVFKXtmpaSkoKSkpAMrI2fAMEJEQlXV6jHvi99wOL1QdClOLSqq/rgtXTV1rSO1tbXYuXNnxxRFToNhRKDc3Fw8/fTTiIiIgFarRVBQEEaPHo1du3YBMP7rQ5IkSJIET09PDBw4EJ999pny+r/+9a/o379/k/dNTU2FJEk4fPiwlb4TovYzGIBP9qUjNa9MdClOrWHLiDlhBGBXDV0/hhGBHnzwQRw6dAjvv/8+Tp8+ja+//hq33HIL8hssgfjKK68gMzMThw4dwuDBgzF+/Hjs3r1bYNVElnV1/Co3yhPM3DBy6623QqUy/gppbTdvorbgRnmCFBYW4ueff8aOHTswatQoAEBkZCSGDBlicp23tzeCgoIQFBSEFStW4MMPP8Q333yD4cOHiyibyOKUdUYMggtxcuaGEV9fXwwZMgR79uzB8ePHcfnyZYSGhnZcgeTQ2DIiiJeXF7y8vLBx40ZUXWvo+lUuLi5wdXVFdXV1B1dHZD2qqy0jXPRMLHPDCADceeedyvHXX39t4YrImThky8igQYOQlZVl9c8NCgpq8wJALi4uWLduHaZPn45Vq1Zh4MCBGDVqFB555BH069evyfXV1dVYsmQJioqKcNtttynPHz16FF5eXibXcvEosicqScJTN9+AHoHeoktxat7eQKdOQEEBkJrattc88MADeOWVVwAAn376KZ5++umOK5AcmkOGkaysLFy+fFl0Gdf04IMPYsyYMfj555+xZ88ebN68Gf/4xz/w73//G1OmTAEAzJ07FwsWLEBlZSW8vLywePFijBkzRnmPnj17NvkXyeXLl3HLLbdY8Tshaj+VSsK8e3qLLoNgbB0pKAAuXQJqawGXa/yG6NevH3r06IHTp09j586dyMrKQlDD5VyJ2sghw4io/xna87lubm644447cMcdd+Dll1/GE088gUWLFilh5Pnnn8eUKVPg5eWFwMBASHWj/a7SaDTKfP86Ltf6CUJkY/ZdKEBUZw8E+LiJLsWpRUYChw4Bej2QkQFERLR+vSRJePjhh/H3v/8dsizjf//7H2bOnGmdYsmhOORvLXveK6FPnz7YuHGj8rW/v3+TsEHkaB5ZnYK/j4vBo0Ov8duPOlTjcSPXCiMAlDACGLtqGEaoPTiAVZD8/Hzcdttt+PDDD/Hbb7/hwoUL+Oyzz/CPf/wD999/v+jyiKxKkiQOYLUB7RnE2rdvX/Tq1QsA8PPPPyMjI6MDKiNHxzAiiJeXF4YOHYp//vOfuPnmm9G3b1+8/PLLmD59Ot555x3R5RFZlUoCVxmxAeauwgrUd9UAxsHzn376qeULI4cnyXYw9aK4uBg6nQ5FRUXw8fExOVdZWYkLFy4gOjoabm7sbyb7wb+79Xos2IwFY3pjUnyU6FKc2sGDQFyc8fiJJ4A1a9r2uhMnTqBPnz4AgB49euDEiRPKgmjk3Fr7/d0Q/7YQkXCBPlq4uahFl+H02tNNAwC9e/fGrbfeCgA4ffo0vv/+ewtXRo6OYYSIhPv5hdvw8OBw0WU4vU6dAE9P47E5YQQAnnnmGeX4rbfesmBV5AwYRoiICIBxn6AbbjAenz8PVFS0/bVjx45F5NWmlc2bN+P06dMdUCE5KoYRIhJu9D9/wif70kSXQQAGDzb+WVsLmLNKglqtxqxZs5Sv3377bQtXRo6MYYSIhMsoqkBJZY3oMgjAiBH1x+ZuED5t2jR4eHgAAFavXo3z589bsDJyZAwjRCScSpJgsPl5fc6h4Ybgu3aZ91o/Pz/Mnj0bgHE/rRdffNGClZEjYxghIuFUEnfttRU9exoHsgLGlhFz/7O8+OKLCAgIAAB89tln2GVuoiGnxDBCRMJJkmT2Lz3qGJJU3zqSnw+YOw7Vx8cHr776qvL1nDlzUFtba8EKyRExjBCRcO9OHIj7YkNEl0FXNRw30p6Gjccffxx9+/YFYNwrbOHChRaqjBwVw4gdkCTJZPO8kydPYtiwYXBzc0P//v2F1dUWO3bsgCRJKCws7LDP2LVrF2JiYuDq6opx48a16zOnTJmCcePGdViN1LphN3RGeCcP0WXQVQ3HjZg7iBUw7hy+Zs0aZQfxpKQkbNmyxULVkSNiGBFkypQpkCQJkiTB1dUVgYGBuOOOO7B27VoYDAaTazMzM3H33XcrXy9atAienp44deoUkpOTrV26WYYPH47MzEzodLoO+4zExET0798fFy5cwLp169r1mcuXL8e6deuUr2+55RbMmTPH8sVSs1buOIfdZ/NEl0FXDR4MXM0R7WoZAYBhw4Zh8eLFytePPfYY1x6hFjGMCHTXXXchMzMTqamp2Lx5M2699VbMnj0b9957r0kfa1BQELRarfL1uXPncNNNNyEyMhKdO3du12dXV1dfd/1todFoEBQUBEmSOuwzzp07h9tuuw1hYWHw9fVt12fqdDr4+vp2WI3Uuvd3p2LvhQLRZdBV7u7AwIHG45Mngdzc9r1PYmIixo4dCwDIy8vDqFGjcOLECQtVSY6EYUQgrVaLoKAghIaGYuDAgZg/fz6++uorbN682eRf6Q27aSRJwoEDB/DKK69AkiT89a9/BQCkp6fj4Ycfhq+vLzp16oT7778fqampynvUdUO89tprCAkJQc+ePc163Ztvvong4GB07twZM2fORE1N/ZoQVVVVmDt3LsLDw6HVatGtWzf85z//AdC0myY/Px8TJkxAaGgoPDw8EBMTg08++cTkvnz++eeIiYmBu7s7OnfujISEBJSVlTW5f6mpqZAkCfn5+Xj88cchSRLWrVvX5DPXrVsHX19fbN26Fb1794aXl5cSBBt/n3XHO3fuxPLly5XWq9TUVOj1ekybNg3R0dFwd3dHz549sXz5cpOaduzYgSFDhsDT0xO+vr4YMWIELpq7rrYTUknGHV/Jdtx8c/1xe9cvq/t/MjY2FgCQlZWFUaNGISUlxQIVkiNhGLExt912G2JjY/HFF180ez4zMxM33ngj/vKXvyAzMxPPPfccampqMHr0aHh7e+Pnn3/Grl27lF+4DVtAkpOTcerUKWzbtg3ffvttm1+3fft2nDt3Dtu3b8f777+PdevWmYSlSZMm4ZNPPsFbb72FEydO4F//+he8vLyarb+yshJxcXHYtGkTjh07hieffBKPPfYY9u3bp3x/EyZMwOOPP44TJ05gx44deOCBB5r9RRUeHo7MzEz4+Phg2bJlyMzMxPjx45v93PLycrz55pv44IMP8NNPPyEtLQ3PPfdcs9cuX74c8fHxmD59OjIzM5GZmYnw8HAYDAaEhYXhs88+w/Hjx7Fw4ULMnz9f2TK9trYW48aNw6hRo/Dbb78hJSUFTz75ZIe2CjkKieuM2JwZMwBXV+Px0qVATk773qdTp05ITk7GwKtNLbm5ubjpppuwcOFCk3/UkJOT2+Gdd96RIyMjZa1WKw8ZMkTeu3dvq9d/+umncs+ePWWtViv37dtX3rRpk1mfV1RUJAOQi4qKmpyrqKiQjx8/LldUVCjPxcXJcmio9R9xcW3/niZPnizff//9zZ4bP3683Lt3b+VrAPKXX36pfB0bGysvWrRI+fqDDz6Qe/bsKRsMBuW5qqoq2d3dXd66davyeYGBgXJVVZXZr4uMjJRra2uVax566CF5/PjxsizL8qlTp2QA8rZt25r9XrZv3y4DkK9cudLivRgzZoz8l7/8RZZlWT5w4IAMQE5NTW3x+sZ0Op383nvvtfiZ7733ngxAPnv2rHLNihUr5MDAQOXrxv89Ro0aJc+ePfuanz1z5kz5wQcflGVZlvPz82UA8o4dO9pUd3N/d53ViMXJ8v9tPiG6DGpk5kxZNq40Istt+N+hVVeuXJFHjhwpA1AeXbt2ldeuXStXV1dbpF6yPa39/m7I7JaRDRs2IDExEYsWLcLBgwcRGxuL0aNHI6eF2Lx7925MmDAB06ZNw6FDhzBu3DiMGzcOx44da1d4aousLODyZes/srIsU78sy2b9a/rIkSM4e/YsvL294eXlBS8vL3Tq1AmVlZU4d+6ccl1MTAw0Go3Zr7vxxhuhVtdv7x4cHKz89z58+DDUajVGjRrVplr1ej1effVVxMTEoFOnTvDy8sLWrVuRlmbclyQ2Nha33347YmJi8NBDD2HNmjW4cuVKm+9FSzw8PNC1a9dmvwdzrFixAnFxcejSpQu8vLywevVqpfZOnTphypQpGD16NMaOHYvly5ebdAVRy+6JCUbf0I4b5Ezt89JLxvEjALByJXDwYPvfy9fXFz/++CNeffVV5efJuXPn8PjjjyMsLAwzZszAtm3bUFJSYoHKyd64mPuCpUuXYvr06Zg6dSoAYNWqVdi0aRPWrl3b7NK/y5cvx1133YXnn38eAPDqq69i27ZteOedd7Bq1arrLL95QUEd8rZW+9wTJ04gOjq6zdeXlpYiLi4OH330UZNzXbp0UY496/YGN/N1rnVttVdJkqTM+HGv+0nVRm+88QaWL1+OZcuWISYmBp6enpgzZ47SLaRWq7Ft2zbs3r0b33//Pd5++2289NJL2Lt3r1n3pLHmvgfZzDEK69evx3PPPYclS5YgPj4e3t7eeOONN7B3717lmvfeew/PPPMMtmzZgg0bNmDBggXYtm0bhg0b1u7ancH8e3qLLoGaERwMzJ4NLF4MVFcDQ4cCL7wAPPII0KMH0GBcfZu4uLhgwYIFuPvuu/Hiiy/ihx9+AADk5ORg5cqVWLlyJVQqFfr27YvevXujR48eCA4Ohr+/v/LQ6XTQarXQaDTKn2q1mt2hds6sMFJdXY0DBw5g3rx5ynMqlQoJCQktDkhKSUlBYmKiyXOjR482WTfD0szZadLW/Pjjjzh69CieffbZNr9m4MCB2LBhAwICAuDj49Phr2soJiYGBoMBO3fuREJCwjWv37VrF+6//3786U9/AgAYDAacPn0affr0Ua6RJAkjRozAiBEjsHDhQkRGRuLLL79s8veoI2k0Guj1+ia1Dx8+HDNmzFCea9iCVGfAgAEYMGAA5s2bh/j4eHz88ccMI9eQmleGszml6OxV33IX2dkTnTw1yC2pwqUr5SbXe7u5oluAF2r1Bhy9XNTk/fqG6uCqVuFcbimKK0zHJYT6uiPAxw1XyqqRmm86MNpdo0avIOP/C4fTC5sE1l5BPnDXqJGWX478siqTcwE+bgj1dUdJZQ3O5pSanHNVq5SWn2OXi1CjN52+3y3AC95urrhcWIGc4kqTc509tYjo7IGKaj1OZhWbnJMkCf3DfQEAJ7OKUVFt+nc2qrMn/Dw1yCmuxOXCCpNzPu6u6NrFCzV6A441cw9jQnVwUavw8LRSfPm1G04dd0FtLfD668aHJAFarQyVGlCpZbioAUllHIysVhkb3WsbLVMAAC4qCUAc9PL38NFVo7KiAtXV9ffSYAB++834aF311YfJHWnyZfsiinMGm+HDf8cvv9wi5LPNCiN5eXnQ6/UIDAw0eT4wMBAnT55s9jVZWVnNXp/VSp9GVVUVqqrq/3IWFxe3eK09q6qqQlZWFvR6PbKzs7FlyxYkJSXh3nvvxaRJk9r8PhMnTsQbb7yB+++/H6+88grCwsJw8eJFfPHFF3jhhRcQFhZm0dc1FBUVhcmTJ+Pxxx/HW2+9hdjYWFy8eBE5OTl4+OGHm1zfvXt3fP7559i9ezf8/PywdOlSZGdnK2Fk7969SE5Oxp133omAgADs3bsXubm56N3buv9yjoqKwt69e5Gamqp0X3Xv3h3//e9/sXXrVkRHR+ODDz7Ar7/+qrTYXLhwAatXr8Z9992HkJAQnDp1CmfOnDHrv6Wzmr3hMI6kF5o8t/ThWDwwMAxbjmXi5a9+Nzk3srs/Ppg2FBU1evzh3aarcu1fkAB/Ly2SvjuJH05km5xbMKY3nhh5A3afy8fMj037HfoE++C72SMBAA+vSkF1o9Dw/bM3o0egN1ZsP4sN+9NNzj19S1fMvasXjl0uxoQ1e0zOBfm4Yc/82wEA0/+7H5lFpoHjk+nDEN+1Mz7ccxErd5gG3IcHheEff4zFpSvlTb5XjVqF068Z1yD6y6dH8HuG6c/Kdx4dgHv7heDrIxn4+ybTKbUJvQPw78mDUVxR0+w9/O2vd8JHrcLSnb+j4u4C6Py6oiilG2AwBg1ZBior635pt/TLu7WRABIA7dVHB5GNg1OobUpLxYUws7tprCEpKQl/+9vfRJfR4bZs2YLg4GC4uLjAz88PsbGxeOuttzB58mSoVG0fzuPh4YGffvoJc+fOxQMPPICSkhKEhobi9ttvb7XFo72va2zlypWYP38+ZsyYgfz8fERERGD+/PnNXrtgwQKcP38eo0ePhoeHB5588kmMGzcORUXGf5n5+Pjgp59+wrJly1BcXIzIyEgsWbLEZNE3a3juuecwefJk9OnTBxUVFbhw4QKeeuopHDp0COPHj4ckSZgwYQJmzJiBzZs3AzDez5MnT+L9999Hfn4+goODMXPmTDz11FNWrd0e/ffxIchq9As6SOcGALi3XwiGRJuup+OhUV/90wVb59yMxnzdjd1yf72vD54f3dPkXBdv4y+/kT38m7xW61L//923z9zUZL+ciKurxD57Rw88fpNpt6Gfp/EzY8N1Td5Xrar/If/BtKHQN5o6FN7J2N05dUQUxvUPNTmnu/q9hHfyaPK+DXsmVjw6EFW1puEp2Nd4Dx8YGIaR3buYnPPUqpX3b+4eemqMvx5e/0MMyscYW1zOny3H95tccfmCC9JS1Sgrl1FVbYBeD+j1EvR6Y00uV39+NW4BAgAXtQQJEvQGQ5MZVGqVdHUHZwOqqmpQW1tjvE6vh8FggGwwQJYNxvsny5BlGTKMf9anDrnh4dUbVR+X5CYn68nNPN3wHjfp2W32fZu+1h7eV5KATp3ERTdJNqPjvLq6Gh4eHvj8889Nls6ePHkyCgsL8dVXXzV5TUREBBITE01Ws1y0aBE2btyII0eONPs5zbWMhIeHo6ioqMkvycrKSly4cAHR0dFwc3Nr67dCJBz/7hKRoysuLoZOp2v293dDZs2m0Wg0iIuLM1mC3GAwIDk5GfHx8c2+Jj4+vsmS5du2bWvxesC4GJiPj4/Jg4iIiByT2d00iYmJmDx5MgYNGoQhQ4Zg2bJlKCsrU2bXTJo0CaGhoUhKSgIAzJ49G6NGjcKSJUswZswYrF+/Hvv378fq1ast+50QERGRXTI7jIwfPx65ublYuHAhsrKy0L9/f2zZskUZpJqWlmYy3mH48OH4+OOPsWDBAsyfPx/du3fHxo0ble2liYiIyLmZNWZElNb6nNjvTvaKf3eJyNF1yJgRIiIiIktzmDBiBw08RCYMzSwIRUTkjGxynRFzuLq6QpIk5ObmokuXLlwSmGyeLMuorq5Gbm4uVCqVyX5BRETOyO7DiFqtRlhYGC5duoTU1FTR5RC1mYeHByIiIsxa4I6IyBHZfRgBAC8vL3Tv3h01NTXXvpjIBqjVari4uLAlj4gIDhJGAOMP94bb3BMREZF9YPswERERCcUwQkREREIxjBAREZFQdjFmpG4NkeLiYsGVEBERUVvV/d6+1lpgdhFGSkpKAADh4eGCKyEiIiJzlZSUQKfTtXjeLvamMRgMyMjIgLe3t0WnQhYXFyM8PBzp6emtrplP14/32np4r62D99l6eK+toyPusyzLKCkpQUhISKtrKtlFy4hKpUJYWFiHvb+Pjw//glsJ77X18F5bB++z9fBeW4el73NrLSJ1OICViIiIhGIYISIiIqGcOoxotVosWrQIWq1WdCkOj/faenivrYP32Xp4r61D5H22iwGsRERE5LicumWEiIiIxGMYISIiIqEYRoiIiEgohhEiIiISyqnDyIoVKxAVFQU3NzcMHToU+/btE12SXUtKSsLgwYPh7e2NgIAAjBs3DqdOnTK5prKyEjNnzkTnzp3h5eWFBx98ENnZ2YIqdgyLFy+GJEmYM2eO8hzvs+VcvnwZf/rTn9C5c2e4u7sjJiYG+/fvV87LsoyFCxciODgY7u7uSEhIwJkzZwRWbJ/0ej1efvllREdHw93dHV27dsWrr75qsqcJ73X7/PTTTxg7dixCQkIgSRI2btxocr4t97WgoAATJ06Ej48PfH19MW3aNJSWllquSNlJrV+/XtZoNPLatWvl33//XZ4+fbrs6+srZ2dniy7Nbo0ePVp+77335GPHjsmHDx+W77nnHjkiIkIuLS1Vrvnzn/8sh4eHy8nJyfL+/fvlYcOGycOHDxdYtX3bt2+fHBUVJffr10+ePXu28jzvs2UUFBTIkZGR8pQpU+S9e/fK58+fl7du3SqfPXtWuWbx4sWyTqeTN27cKB85ckS+77775OjoaLmiokJg5fbntddekzt37ix/++238oULF+TPPvtM9vLykpcvX65cw3vdPt9995380ksvyV988YUMQP7yyy9Nzrflvt51111ybGysvGfPHvnnn3+Wu3XrJk+YMMFiNTptGBkyZIg8c+ZM5Wu9Xi+HhITISUlJAqtyLDk5OTIAeefOnbIsy3JhYaHs6uoqf/bZZ8o1J06ckAHIKSkposq0WyUlJXL37t3lbdu2yaNGjVLCCO+z5cydO1e+6aabWjxvMBjkoKAg+Y033lCeKywslLVarfzJJ59Yo0SHMWbMGPnxxx83ee6BBx6QJ06cKMsy77WlNA4jbbmvx48flwHIv/76q3LN5s2bZUmS5MuXL1ukLqfspqmursaBAweQkJCgPKdSqZCQkICUlBSBlTmWoqIiAECnTp0AAAcOHEBNTY3Jfe/VqxciIiJ439th5syZGDNmjMn9BHifLenrr7/GoEGD8NBDDyEgIAADBgzAmjVrlPMXLlxAVlaWyb3W6XQYOnQo77WZhg8fjuTkZJw+fRoAcOTIEfzyyy+4++67AfBed5S23NeUlBT4+vpi0KBByjUJCQlQqVTYu3evReqwi43yLC0vLw96vR6BgYEmzwcGBuLkyZOCqnIsBoMBc+bMwYgRI9C3b18AQFZWFjQaDXx9fU2uDQwMRFZWloAq7df69etx8OBB/Prrr03O8T5bzvnz57Fy5UokJiZi/vz5+PXXX/HMM89Ao9Fg8uTJyv1s7mcJ77V5XnzxRRQXF6NXr15Qq9XQ6/V47bXXMHHiRADgve4gbbmvWVlZCAgIMDnv4uKCTp06WezeO2UYoY43c+ZMHDt2DL/88ovoUhxOeno6Zs+ejW3btsHNzU10OQ7NYDBg0KBBeP311wEAAwYMwLFjx7Bq1SpMnjxZcHWO5dNPP8VHH32Ejz/+GDfeeCMOHz6MOXPmICQkhPfaCThlN42/vz/UanWT2QXZ2dkICgoSVJXjmDVrFr799lts374dYWFhyvNBQUGorq5GYWGhyfW87+Y5cOAAcnJyMHDgQLi4uMDFxQU7d+7EW2+9BRcXFwQGBvI+W0hwcDD69Olj8lzv3r2RlpYGAMr95M+S6/f888/jxRdfxCOPPIKYmBg89thjePbZZ5GUlASA97qjtOW+BgUFIScnx+R8bW0tCgoKLHbvnTKMaDQaxMXFITk5WXnOYDAgOTkZ8fHxAiuzb7IsY9asWfjyyy/x448/Ijo62uR8XFwcXF1dTe77qVOnkJaWxvtuhttvvx1Hjx7F4cOHlcegQYMwceJE5Zj32TJGjBjRZHr66dOnERkZCQCIjo5GUFCQyb0uLi7G3r17ea/NVF5eDpXK9FeSWq2GwWAAwHvdUdpyX+Pj41FYWIgDBw4o1/z4448wGAwYOnSoZQqxyDBYO7R+/XpZq9XK69atk48fPy4/+eSTsq+vr5yVlSW6NLv19NNPyzqdTt6xY4ecmZmpPMrLy5Vr/vznP8sRERHyjz/+KO/fv1+Oj4+X4+PjBVbtGBrOppFl3mdL2bdvn+zi4iK/9tpr8pkzZ+SPPvpI9vDwkD/88EPlmsWLF8u+vr7yV199Jf/222/y/fffz+mm7TB58mQ5NDRUmdr7xRdfyP7+/vILL7ygXMN73T4lJSXyoUOH5EOHDskA5KVLl8qHDh2SL168KMty2+7rXXfdJQ8YMEDeu3ev/Msvv8jdu3fn1F5Lefvtt+WIiAhZo9HIQ4YMkffs2SO6JLsGoNnHe++9p1xTUVEhz5gxQ/bz85M9PDzkP/zhD3JmZqa4oh1E4zDC+2w533zzjdy3b19Zq9XKvXr1klevXm1y3mAwyC+//LIcGBgoa7Va+fbbb5dPnTolqFr7VVxcLM+ePVuOiIiQ3dzc5BtuuEF+6aWX5KqqKuUa3uv22b59e7M/mydPnizLctvua35+vjxhwgTZy8tL9vHxkadOnSqXlJRYrEZJlhssb0dERERkZU45ZoSIiIhsB8MIERERCcUwQkREREIxjBAREZFQDCNEREQkFMMIERERCcUwQkREREIxjBAREZFQDCNEREQkFMMIERERCcUwQkREREIxjBAREZFQ/x9YV3G3sVHniQAAAABJRU5ErkJggg==\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(x,U[0], label='tiempo = 0', linestyle = 'dashed', linewidth = 1)\n", "plt.plot(x,U[-1], label='SPH', color = 'black', linewidth = 2)\n", "plt.plot(x,u_res[-1], label='Diferencias finitas', color = 'blue', linewidth = 2)\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "id": "VSb_3AfO0DMp" }, "source": [ "Podemos ver que el método de SPH se asemeja al obtenido por el método de las diferencias finitas, sin embargo es claramente más difusivo y mucho mas lento!. " ] }, { "cell_type": "markdown", "metadata": { "id": "KG-pJVT7KLpl" }, "source": [ "Como se comentó anteriormente es posible mejorar la aproximación a las derivadas. Haciendo una expansión de series de taylor, se puede obtener una aproximación de orden superior a la obtenida inicialmente.\n", "\\begin{equation}\n", "\\nabla f_j \\approx \\left[ \\nabla f_j \\right] - \\left[ f_j \\nabla 1 \\right] = \\sum_j (f_j - f_i) \\nabla W_{ij} \\Delta x\n", "\\end{equation}\n", "La implementación es sumamente simple (sólo dos lineas de código), y se realiza a continuación de acuerdo a la aproximación que teniamos anteriormente." ] }, { "cell_type": "code", "execution_count": 49, "metadata": { "id": "__RlRiSSInnx" }, "outputs": [], "source": [ "def daprox3(f_i,x_i,x,h,option=1,fulloutput=False, f0=0,fN=0):\n", " \"\"\" option = 0 fi = dado con f0 a la izq, y fN a la der.\n", " option = 1 fi = cte (grad 0)\n", " option = 2 reflejo\n", " option = 3 -reflejo \"\"\"\n", "\n", " x0 = x_i[0] #distancia inicial \n", " xN = x_i[-1] #distancia final\n", " dx = x_i[1]-x0 #dx en este caso es constante, pero puede no serlo.\n", " particulas_nuevas = int(np.ceil(h/dx))+1 # para agregar particulas\n", " x0_new = x0-particulas_nuevas*dx #distancia extendida a la izquierda\n", " xN_new = xN+particulas_nuevas*dx # distancia extendida a la derecha\n", " x_left = np.arange(x0_new,x0,dx)\n", " x_right = np.arange(xN+dx,xN_new+dx,dx)\n", " if option == 1:\n", " fi_left = np.ones_like(x_left) * f_i[0]\n", " fi_right = np.ones_like(x_right) * f_i[-1]\n", " elif option ==2:\n", " fi_left = np.flip(f_i[1:particulas_nuevas+1])\n", " fi_right = np.flip(f_i[len(f_i) - particulas_nuevas-1:-1])\n", " elif option ==3:\n", " fi_left = np.flip(f_i[1:particulas_nuevas+1]) * -1\n", " fi_right = np.flip(f_i[len(f_i) - particulas_nuevas-1:-1]) * -1\n", " else:\n", " fi_left = np.ones_like(x_left) * f0\n", " fi_right = np.ones_like(x_right) * fN\n", "\n", " x_i_new = np.concatenate((x_left,x_i,x_right))\n", " f_i_new = np.concatenate((fi_left,f_i,fi_right))\n", "\n", " df_new = []\n", " for i,xx in enumerate(x): #loop para cada valor de x\n", " dW_i = dcubic(xx-x_i_new, h, 1)\n", " fj_menos_fi = f_i_new-f_i[i] \n", " df_new.append(np.dot(dW_i,fj_menos_fi)*dx) \n", " if fulloutput:\n", " return x_i_new,f_i_new,np.nan_to_num(df_new)\n", " else:\n", " return np.nan_to_num(df_new)" ] }, { "cell_type": "code", "execution_count": 50, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 265 }, "id": "eItuTv8IRVjz", "outputId": "773dc982-9c55-4f51-bd42-993de60f29b3" }, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "\n", "U2 = []\n", "U2.append(U[0])\n", "u = U[0]\n", "\n", "for t in tiempo:\n", " du = daprox3(u,x,x,h,option=1,f0=u0,fN=uN)\n", " unew = aprox(u,x,x,h,option=1,f0=u0,fN=uN) - c*du*dt\n", " unew[0] = u0\n", " unew[-1] = uN\n", " U2.append(unew)\n", " u = unew\n", "plt.plot(x,U2[-1], label='Gradiente mejorado', color = 'black')\n", "plt.plot(x,U[-1], label='Gradiente simple', linestyle= 'dashed')\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "id": "Iy4iPKF9_lpd" }, "source": [ "Mejoría pero marginal" ] }, { "cell_type": "markdown", "metadata": { "id": "D9tACKpr264F" }, "source": [ "Vamos a resolver un problema 1D real. Correspondiente a un problema complejo de resolver para los método tradicionales. El modelo corresponde al vaciado de un estanque. \n" ] }, { "cell_type": "markdown", "metadata": { "id": "QqZ9LgB6S3TP" }, "source": [ "-------------------------------------" ] }, { "cell_type": "markdown", "metadata": { "id": "d45SA4Nr0GxF" }, "source": [ "ELproblema corresponde al estudio realizado en una instalación experimental. La instalación se detalla en la sigueinte publicación:\n", "
\n", "Paper: Liou, Chyr Pyng, and William A. Hunt. \"Filling of pipelines with undulating elevation profiles.\" Journal of Hydraulic Engineering 122.10 (1996): 534-539.\n", "
\n", "\n", "La siguiente solución sigue varias de las recomendaciones, publicada en el siguiente artículo.\n", "\n", "
\n", "Paper:Hou, Q., Zhang, L. X., Tijsseling, A. S., & Kruisbrink, A. C. H. (2012). Rapid filling of pipelines with the SPH particle method. Procedia Engineering, 31, 38-43.\n", "
" ] }, { "cell_type": "markdown", "metadata": { "id": "EsPKYPkt3fC1" }, "source": [ "El sistema de cuaciones del problema se presenta a continuación:" ] }, { "cell_type": "markdown", "metadata": { "id": "3SPojF_XFxXu" }, "source": [ "\n", "\n", "$$\\frac{dP}{dt} = \\rho c^2 \\frac{dV}{dx} \\tag{p1-1}$$\n", "\n", "$$\\frac{dV}{dt} = -\\frac{1}{\\rho} \\frac{dP}{dx} + g \\sin(\\theta) - \\lambda \\frac{v |v|}{2D} \\tag{p1-2}$$\n", "\n", "$$\\frac{dx}{dt} = V \\tag{p1-3}$$\n", "\n", "donde $P$ = presion, $V$ = velocidad, $\\rho$ = densidad del agua, $c$= velocidad del sonido en el agua, $g$ = aceleración de gravedad, $\\theta$ = ángulo de inclinación de la tubertía, $\\lambda$ = factor de fricción deDarcy-Weisbach, $D$ = Diametro de la tuberia, x y t es la coordenada espacial y la temporal, respectivamente; y $D\\cdot/dt$ es la derivada material, ya que vamos a advectar las partículas, y por lo tanto estamos en un marco referencial lagrangiano." ] }, { "cell_type": "markdown", "metadata": { "id": "B_9kMVeO1ubg" }, "source": [ "Las condiciones inicial es:\n", "$$ V(x,0) = 0 \\tag{p1-4a}$$\n", "\n", "$$ P(x,0) = \\rho g \\left( H_r + x\\sin(\\theta) \\right) \\tag{p1-4b} $$\n", "\n", "y la condición de borde es:\n", "\n", "$$P(0,t) = \\rho g (Hr - \\frac{V^2}{2g} + K \\frac{V^2}{2g}) \\quad \\text{ y } \\quad P(L(t),t) = 0 \\tag{p1-5a y p1-5b} $$\n", "\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "id": "560h1lpP1tL3" }, "outputs": [], "source": [] }, { "cell_type": "markdown", "metadata": { "id": "3FVZo4l27Y2f" }, "source": [ "En SPH se puede escribir la ecuación p1-1, p1-2:\n" ] }, { "cell_type": "markdown", "metadata": { "id": "2jv21Emj7fme" }, "source": [ "$$\\frac{P_a}{dt} = -c^2 \\sum_b m_b (V_a - V_b) \\frac{dWab}{dx_a}$$\n", "\n", "$$\\frac{V_a}{dt} = - \\frac{1}{\\rho^2} \\sum_b m_b (P_a - P_b + \\Pi_{ab}) \\frac{dWab}{dx_a} + g \\sin(\\theta) - \\lambda \\frac{V_a \\left| v \\right|}{2D}$$\n", "\n", "$$ \\frac{dx_a}{dt} = V_a$$" ] }, { "cell_type": "code", "execution_count": 51, "metadata": { "id": "reQrdxbw9kRf" }, "outputs": [], "source": [ "### pasos\n", "### HINT agregamos particulas a medida que salen\n", "### generamos particulas vecinas en los bordes para mantener la consistencia del kernel la candidad particulas es entonces (~2h/dx)\n", "### idem para las particulas externas hasta que salen de la tubería. (donde las eliminamos)" ] }, { "cell_type": "markdown", "metadata": { "id": "N4bXRjJOhRkP" }, "source": [ "Es muy usual en el uso de esta técnica para estabilizar el modelo, el uso de una viscosidad artificial, la cual se incorpora en la ecuación de momentum.\n", "La ecuación tipica es de la forma: " ] }, { "cell_type": "markdown", "metadata": { "id": "WlYc5YcX9cqF" }, "source": [ "$$\\Pi_{ab} = \\frac{-ch}{\\rho} \\min \\left[ \\frac{(V_a -V_b)(x_a - x_b)}{r_{ab}^2 + 0.01 h^2} ; 0.0 \\right] $$" ] }, { "cell_type": "code", "execution_count": 52, "metadata": { "id": "Gr3E1mDb33c-" }, "outputs": [], "source": [ "## funcion PI\n", "def PI_ab(Va,Vb,Xa,Xb,h,rho,c):\n", " ss = np.abs((Xa-Xb))**2+0.01*h**2 \n", " aa = (Va-Vb)*(Xa-Xb)/ss\n", " bb = np.zeros_like(aa,dtype=np.float64)\n", " cc = - np.min([aa,bb],axis=0) *c*h/rho\n", " return cc\n", "\n", "### la derivada del kernel\n", "def dwab_dxa(xa,xb,h):\n", " dd = xa-xb\n", " rab = np.abs(dd)\n", " f1 = np.sign(dd)/h**2\n", " q = rab/h\n", " sal = np.zeros_like(f1,dtype=np.float64)\n", " #q<1:\n", " sal[q<1] = -2*q[q<1]+1.5*q[q<1]**2\n", " # 1<=q<=2:\n", " sal[(q>=1)&(q<=2)] = -0.5*(2-q[(q>=1)&(q<=2)])**2\n", " return f1 * sal\n", "\n", "## h aca es variable para mantener las vecinas\n", "def hvecinas(X,ind,vecinas):\n", " Xa = X[ind]\n", " h = (X[ind+vecinas]-X[ind-vecinas])/4\n", " return np.abs(h)\n" ] }, { "cell_type": "markdown", "metadata": { "id": "dA41PZUU9414" }, "source": [ "El esquema siguiente resume la conceptualización del problema. \n", "![image](https://docs.google.com/drawings/d/e/2PACX-1vSPr763TPP-qlMBycSF1zFoHsPbU0b1yK8gqMDgmTOf5-igw6KAFeMdFlNlCNls74bW2vktZn1uk6rC/pub?w=920&h=600)" ] }, { "cell_type": "markdown", "metadata": { "id": "fw9biAJ_1a8t" }, "source": [ "La idea es crear partículas a medida que el fluido avanza. Las particulas grises son nuestra condición de borde. Definen condiciones constantes del problema. Las de la derecha representan la presión atmosférica. Las del izquierda la presión justo a la entrada de la tubería. \n", "Introducimos las variables del problema. Además de los parámetros necesarios para el postproceso." ] }, { "cell_type": "code", "execution_count": 53, "metadata": { "id": "cPSXQXjpBNnV" }, "outputs": [], "source": [ "### Variables del problema \n", "## paper: FILLING OF PIPELINES WITH UNDULATING ELEVATION PROFILES 1996 \n", "### del problema\n", "\n", "rho = 1000\n", "Hr = 0.354\n", "c = 1000 #m/s\n", "c = 200 # m/s\n", "theta = 0*np.pi/180.0 ##notar que por la formula la fuerza acelera el movimiento\n", "Ltub = 6.7 #m\n", "fric_fac = 0.03 # DW-Colebrook-White\n", "K_loss = 0.9\n", "D = 22.9 #mm\n", "Tiempo_total = 1.0 #seg\n", "g = 9.81\n", "Patm = 10*rho*g*0\n", "### Discretizacion\n", "dx = 0.03 #m\n", "#Ampli = 5 # particulas totales (Ampli veces el largo del tub) \n", "courant = 0.5\n", "vecinas = 3\n", "\n", "### De la simulacion\n", "outputTime = 0.5 ## imprime cada 1 segundo" ] }, { "cell_type": "code", "execution_count": 54, "metadata": { "id": "BHOSmcHyDXFU" }, "outputs": [], "source": [ "## unidades y constantes\n", "D= D/1000.\n", "A_tub = np.pi*(D/2)**2\n", "vol = A_tub*dx\n", "#mb = vol*rho\n", "mb = dx*rho\n", "h = 1.5*dx\n", "tiempo = 0\n", "DT_ini = dx/c*courant # seg" ] }, { "cell_type": "markdown", "metadata": { "id": "fRL5jVf7JVPh" }, "source": [ "Desde el punto de vista de la programación, existen varias estrategias para realizar el marco conceptual de la solución, los dos marcos son programación orientada al objeto, y programación funcional. . En este caso, seguiremos el segundo enfoque y vamos a usar arreglos de numpy para fines educativos. Por eficiencia es mejor no crear varias particulas." ] }, { "cell_type": "code", "execution_count": 55, "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "_JlfRJCg-829", "outputId": "7a4a53c1-d150-4f02-be03-7f866c0c4932" }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "el numero de partículas inicialmente es: 8\n" ] } ], "source": [ "#Definimos el numero inicial de particulas\n", "Np = int(2*vecinas+2)\n", "print(\"el numero de partículas inicialmente es: \", Np)" ] }, { "cell_type": "markdown", "metadata": { "id": "-FJbVf2k3elm" }, "source": [ "Para cada una de las particulas, creamos arreglos con las variables que vamos a utilizar, la velocidad, la presión. Como condición inicial, la velocidad es 0, y la presión es la presión hidroestática más la presión atmosférica. Además guardamos los resultados de las ecuaciones que vamos a resolver dPa y dVa (ver las ulltimas ecuaciones)." ] }, { "cell_type": "code", "execution_count": 56, "metadata": { "id": "0d8RqBSMJwHg" }, "outputs": [], "source": [ "#creamos los arreglos para guardar las variables que represetan las particulas\n", "\n", "VV = np.zeros(Np)\n", "PP = np.ones(Np)*g*rho*Hr + Patm\n", "dPa = np.zeros(Np)\n", "dVa = np.zeros(Np)" ] }, { "cell_type": "code", "execution_count": 57, "metadata": { "id": "vZ3xpDDrJTRZ" }, "outputs": [], "source": [ "## Condicion inicial\n", "## en L(0)\n", "if tiempo == 0:\n", " Part_total = 2*vecinas + 2\n", " XX = np.linspace(-(vecinas +1)*dx,vecinas*dx,Np) #coordenada x de c/part.\n", " PP[vecinas+1:] = Patm\n", " Particulas_activas = np.array([vecinas,vecinas+1]) # al inicio es solo 2\n", " DT = DT_ini\n", "\n", " \n", " # indice de las particulas en los bordes\n", " Part_saliente = Particulas_activas[1]\n", " Part_entrante = Particulas_activas[0]\n", " PP[Part_saliente] = Hr*g*rho/2 + Patm\n", " \n" ] }, { "cell_type": "markdown", "metadata": { "id": "IQ22P3YsLWrO" }, "source": [ "La condición inicial se puede entender mejor en el siguiente esquema.\n", "\n", "![imagen](https://docs.google.com/drawings/d/e/2PACX-1vR3ta7mO85G88erhAcSFUpKW8TuUSfomDmE9k4j58B1PVVJc50uGDWb7VW95qr1JGn0TeOj93sVmpPU/pub?w=500&h=480)" ] }, { "cell_type": "code", "execution_count": 58, "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "V1HiN_lVCQE_", "outputId": "21c1160a-b287-4360-ea7e-be13b6a6e3b5" }, "outputs": [ { "data": { "text/plain": [ "array([3472.74, 3472.74, 3472.74, 3472.74, 1736.37, 0. , 0. ,\n", " 0. ])" ] }, "execution_count": 58, "metadata": {}, "output_type": "execute_result" } ], "source": [ "PP" ] }, { "cell_type": "code", "execution_count": 59, "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "2brH-9V2_AXb", "outputId": "bd0f89a8-e233-440d-a432-f6c83d6d8348" }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "============== t = 7.499903536240717e-05 seg. =============\n", "dt : 7.5e-05 Pas.\n", "presion máxima : 3472.7375 Pas.\n", "Vel máxima : 0.003 m/s.\n", "posición del frente: 0.0 m.\n", "# Particulas activas: 2 \n", "============== t = 0.5000343006185194 seg. =============\n", "dt : 7.211e-05 Pas.\n", "presion máxima : 971.3908 Pas.\n", "Vel máxima : 1.624 m/s.\n", "posición del frente: 0.797 m.\n", "# Particulas activas: 27 \n", "tiempo de ejecución: 67.16541790962219 seg\n" ] } ], "source": [ "inicio = time.time()\n", "### Loop en el tiempo\n", "print_time = 0\n", "res_x = []\n", "res_P = []\n", "res_V = []\n", "while tiempo <= Tiempo_total:\n", " #output\n", " if tiempo > print_time:\n", " print (f\"============== t = {tiempo} seg. =============\")\n", " print (f\"dt : {np.round(DT,8)} Pas.\" )\n", " print (f\"presion máxima : {np.round(np.max(PP),4)} Pas.\" )\n", " print (f\"Vel máxima : {np.round(np.max(VV),3)} m/s.\" )\n", " print (f\"posición del frente: {np.round(X_sale,3)} m.\" )\n", " print (f\"# Particulas activas: {len(Particulas_activas)} \" )\n", " #print (f\"aceleracion : {dvatemp[Particulas_activas]}\")\n", " #print (f\"roce:\" , roce)\n", " #print (f\"dvatemp : {dpatemp[Particulas_activas]}\")\n", " print_time += outputTime\n", " res_x.append(XX)\n", " res_P.append(PP)\n", " res_V.append(VV)\n", "\n", "\n", " #print(\"tiempo =\",tiempo)\n", " # Update Presion (ec p1-6)\n", " ## Pa/dt\n", " for particula in Particulas_activas:\n", " Xa = XX[particula]\n", " Xb = XX\n", " Va = VV[particula]\n", " Vb = VV\n", " ha = hvecinas(XX,particula,vecinas)\n", " dW_i = dwab_dxa(Xa,Xb,ha)\n", " fj_menos_fi = Va - Vb\n", " dPa[particula] = -c**2 * np.dot(dW_i,fj_menos_fi)*mb\n", "\n", "\n", "\n", "\n", " ## euler time\n", " ##PP = PP - dPa*DT\n", " ## rungeKuta 2nd\n", " dpatemp = dPa \n", " PP1 = PP - dPa*DT/2\n", " PP = (PP + PP1 - dPa*DT)/2\n", "\n", "\n", " #print(np.max(PP))\n", " #Updat+\n", " ## Va/dt\n", " for particula in Particulas_activas:\n", " Xa = XX[particula]\n", " Xb = XX\n", " Pa = PP[particula]\n", " Pb = PP\n", " Va = VV[particula]\n", " Vb = VV\n", " ha = hvecinas(Xb,particula,vecinas)\n", " dW_i = dwab_dxa(Xa,Xb,ha)\n", " PII = PI_ab(Va,Vb,Xa,Xb,ha,rho,c)\n", " fj_menos_fi = Pa - Pb + PII\n", " da1 = -1/rho**2 * np.dot(fj_menos_fi,dW_i)*mb\n", " roce = fric_fac*Va*np.abs(Va)/2/D\n", " dVa[particula] = da1 + roce + g*np.sin(theta)\n", " \n", "\n", "\n", "## Va = Va - Va/dt *DT\n", " #print(da1)\n", " VV1 = VV - dVa*DT/2\n", " VV = (VV + VV1 - dVa*DT)/2\n", " dvatemp = dVa\n", "\n", "\n", "## corregimos las particulas vecinas ficticias\n", " #en el estanque\n", " Ve = VV[Part_entrante]\n", " Ecine = Ve**2/2/g\n", " VV[XX < XX[Part_entrante]] = Ve\n", " PP[XX <= XX[Part_entrante]] = (Hr - (1+K_loss)*Ecine)*rho*g + Patm\n", " ## hacia la salida\n", " Vs = VV[Part_saliente]\n", " VV[XX>XX[Part_saliente]] = Vs\n", " PP[XX>=XX[Part_saliente]] = Patm\n", "\n", " ##Update Xa\n", " XX = XX + VV*DT\n", " #XX = (XX +VV*DT)/2\n", " #XX[XX>XX[Part_saliente]] = XX[XX>XX[Part_saliente]] + VV[Part_saliente]*DT\n", "\n", " ## Creamos particulas faltantes y activamos las que correspondan\n", " ### Update las particulas activas\n", " # Particulas nuevas que entran\n", " X_entra = XX[Part_entrante]\n", " X_sale = XX[Part_saliente]\n", " \n", "\n", " Pnew = np.argwhere((XX < X_entra ) & (XX >= 0))\n", " if len(Pnew) > 0:\n", " #print(X_sale)\n", " X_new_entrante = np.min(XX[Pnew[0]])\n", " ## agregamos particulas ficiticas al arreglo\n", " #print(\"Coordenada del particula entrante:\", X_new_entrante)\n", "\n", " Part_fict = len(Pnew) # cantidad de particulas activas en la tub\n", " Xmin = np.min(XX)\n", " XNuevas = np.linspace(Xmin -Part_fict*dx , Xmin, num=Part_fict)\n", " PNuevas = (np.ones_like(XNuevas) * (Hr - Ecine*(1 - K_loss))*rho*g) + Patm\n", " VNuevas = np.zeros_like(XNuevas) + Ve\n", " #print(dPa)\n", " #print(dVa)\n", " XX = np.concatenate((XNuevas,XX), axis=None)\n", " PP = np.concatenate((PNuevas,PP), axis=None)\n", " VV = np.concatenate((VNuevas,VV), axis=None)\n", " \n", "\n", " Part_entrante = np.searchsorted(XX, X_new_entrante, side=\"left\")\n", " Part_saliente = np.searchsorted(XX, X_sale, side=\"left\")\n", " #print(\"la Coordenada de la particula saliente es \",\n", " # np.round(X_sale,4))\n", " \n", " if X_sale <= Ltub:\n", " Particulas_activas = np.flatnonzero((XX>=X_new_entrante) & (XX<=X_sale))\n", " #Particulas_activas = np.argwhere((XX>=X_new_entrante) & (XX<=X_sale))\n", "\n", " else:\n", " #print(\"Flujo llega al fin tuberia!\")\n", " #salen particulas para afuera\n", " #identifiquemos las mas alejadas\n", " Psalen = np.flatnonzero((XX > Ltub + vecinas*dx ))\n", " #las sacamos de las matrices\n", " XX = np.delete(XX,Psalen)\n", " PP = np.delete(PP,Psalen)\n", " VV = np.delete(VV,Psalen)\n", " #pasan a ser activas las que estan dentro de los limites\n", " Particulas_activas = np.flatnonzero((XX>=X_new_entrante) & (XX<=Ltub))\n", " Xmax_activo = np.max(XX[Particulas_activas]) \n", " Part_saliente = np.searchsorted(XX, Xmax_activo, side=\"left\")\n", " #finalmente actualizamos los indices de las particulas limites\n", " \n", " dPa = np.zeros(len(VV))\n", " dVa = np.zeros(len(VV))\n", "\n", " #calculo del dt\n", " Dxx = (XX[1:]-XX[:-1])\n", " Dxx_min = np.min(Dxx)\n", " if Dxx_min < 0 :\n", " print(\"Dx es negativo: error\")\n", " DT = 1e6\n", " else:\n", " DT = Dxx_min/(c+np.max(VV))*courant\n", "\n", " #print(tiempo, DT)\n", "\n", "### loop\n", " tiempo = tiempo + DT\n", "fin = time.time()\n", "print(\"tiempo de ejecución: \", fin-inicio, \"seg\")" ] }, { "cell_type": "markdown", "metadata": { "id": "fet9qo4dTB9g" }, "source": [ "Veamos la cantidad de particulas consultando la variable velocidad." ] }, { "cell_type": "code", "execution_count": 60, "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "mmRQ_B1o4nNI", "outputId": "e9d99166-2bd6-40fc-c717-3b43d458ccb9" }, "outputs": [ { "data": { "text/plain": [ "58" ] }, "execution_count": 60, "metadata": {}, "output_type": "execute_result" } ], "source": [ "VV.size" ] }, { "cell_type": "markdown", "metadata": { "id": "VO1WkGt-TNOf" }, "source": [ "Este código fue programado mezclando aspectos de python y numpy. Es sabido que python en comparación con otros lenguajes es lento, y esto pasa básicamente porque es un lenguaje que va interpretando linea por linea de código. Los lenguajes de programación que se compilan son más eficientes que python, incluso en varios ordenes de magnitud, siendo C (y sus variantes) y Fortran, los preferidos para métodos numéricos.\n", "Ahora existen varios proyectos que buscan acelerar los códigos en python. En esta ocación vamos a referirnos a la libería numba. Apliquemosla a nuestro código. " ] }, { "cell_type": "code", "execution_count": 61, "metadata": { "id": "19fQ0nZMeR9K" }, "outputs": [], "source": [ "### Optimizado\n", "from numba import *\n", "\n", "@jit\n", "def PI_ab(Va,Vb,Xa,Xb,h,rho,c):\n", " N = Xb.size\n", " ss = (Xa-Xb)*(Xa-Xb)+0.01*h*h\n", " aa = (Va-Vb)*(Xa-Xb)/ss\n", " bb = np.zeros(N,dtype=np.float64)\n", " temp = np.array([aa,bb])\n", " cc = np.min(temp,axis=0) *c*h/rho\n", " return -cc\n", "\n", "@jit\n", "def dwab_dxa(xa,xb,h):\n", " N = xb.size\n", " dd = xa-xb\n", " rab = np.abs(dd)\n", " f1 = np.sign(dd)/h/h\n", " q = rab/h\n", " sal = np.zeros(N,dtype=np.float64)\n", " ff = q < 1\n", " sal[ff] = -2*q[ff]+1.5*q[ff]**2\n", " ff1 = (q>=1)&(q<=2)\n", " sal[ff1] = -0.5*(2-q[ff1])**2\n", " return f1 * sal\n", "\n", "@jit\n", "def hvecinas(X,ind,vecinas):\n", " Xa = X[ind]\n", " h = (X[ind+vecinas]-X[ind-vecinas])/4\n", " return np.abs(h)\n", "\n", "@jit\n", "def DeltaPress(Particulas,vecinas,X,V,c,mb):\n", " N = X.size\n", " dPa = np.zeros(N, dtype=np.float64)\n", " for particula in Particulas:\n", " Xa = X[particula]\n", " pos_iz = particula - vecinas\n", " pos_der = particula + vecinas + 1\n", " Xb = X[pos_iz:pos_der]\n", " Va = V[particula]\n", " Vb = V[pos_iz:pos_der]\n", " ha = hvecinas(Xb,vecinas,vecinas)\n", " dW_i = dwab_dxa(Xa,Xb,ha)\n", " fj_menos_fi = Va - Vb\n", " dPa[particula] = -c**2 * np.dot(dW_i,fj_menos_fi)*mb\n", " return dPa\n", "\n", "@jit\n", "def DeltaVel(Particulas,vecinas,X,V,P,c,mb,theta,D,fric_fac,rho,g):\n", " N = X.size\n", " dVa = np.zeros(N, dtype=np.float64)\n", " for particula in Particulas:\n", " pos_iz = particula - vecinas\n", " pos_der = particula + vecinas +1\n", " \n", " Xa = X[particula]\n", " Pa = P[particula]\n", " Va = V[particula]\n", "\n", " Xb = X[pos_iz:pos_der]\n", " Pb = P[pos_iz:pos_der]\n", " Vb = V[pos_iz:pos_der]\n", "\n", " ha = hvecinas(Xb,vecinas,vecinas)\n", " dW_i = dwab_dxa(Xa,Xb,ha)\n", " PII = PI_ab(Va,Vb,Xa,Xb,ha,rho,c)\n", " fj_menos_fi = Pa - Pb + PII\n", " da1 = -1/rho/rho * np.dot(fj_menos_fi,dW_i)*mb\n", " roce = fric_fac*Va*np.abs(Va)/2/D\n", " dVa[particula] = da1 + roce + g*np.sin(theta)\n", " return dVa " ] }, { "cell_type": "markdown", "metadata": { "id": "ffbg0QWkT85r" }, "source": [ "Primero vemos que el código es el mismo, y que lo único que se ha añadido es una linea que empieza con \"@jit\" " ] }, { "cell_type": "markdown", "metadata": { "id": "1TU3-vtsUIdG" }, "source": [ "Esto recibe el nombre de decorador, y es como se puede ver, no significa nada en lo que hemos programado. Esta forma simple de implementación permite acelerar una función, siempre y cuando este programada en python (es decir sin otras liberias) y con numpy. A la fecha todavía no es útil para otras librerías como pandas. " ] }, { "cell_type": "code", "execution_count": 62, "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "2lB4qSQo9Evp", "outputId": "a23dfaae-5c97-4167-e235-4aa70d635d65" }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "el numero de partículas inicialmente es: 8\n" ] } ], "source": [ "### Variables del problema \n", "## paper: FILLING OF PIPELINES WI´TH UNDULATING ELEVATION PROFILES 1996 \n", "### del problema\n", "\n", "\n", "rho = 1000\n", "Hr = 0.354\n", "#c = 1000 #m/s\n", "c = 200 # m/s\n", "theta = 0*np.pi/180.0 ##notar que por la formula la fuerza acelera el movimiento\n", "Ltub = 6.7 #m\n", "fric_fac = 0.03 # DW-Colebrook-White\n", "K_loss = 0.9\n", "D = 22.9 #mm\n", "Tiempo_total = 7.0 #seg\n", "g = 9.81\n", "Patm = 10*rho*g*0\n", "### Discretizacion\n", "dx = 0.03 #m\n", "#Ampli = 5 # particulas totales (Ampli veces el largo del tub) \n", "courant = 0.5\n", "vecinas = 3\n", "### De la simulacion\n", "outputTime = 0.5 ## imprime cada 1 segundo\n", "## unidades y constantes\n", "D= D/1000.\n", "A_tub = np.pi*(D/2)**2\n", "vol = A_tub*dx\n", "#mb = vol*rho\n", "mb = dx*rho\n", "h = 1.5*dx\n", "tiempo = 0\n", "DT_ini = dx/c*courant # seg\n", "#Definimos el numero de particulas\n", "Np = int(2*vecinas+2)\n", "print(\"el numero de partículas inicialmente es: \", Np)" ] }, { "cell_type": "code", "execution_count": 63, "metadata": { "id": "RIBEubtH-RAM" }, "outputs": [], "source": [ "if tiempo == 0:\n", " VV = np.zeros(Np)\n", " PP = np.ones(Np)*g*rho*Hr + Patm\n", " dPa = np.zeros(Np)\n", " dVa = np.zeros(Np)\n", " Part_total = 2*vecinas + 2\n", " XX = np.linspace(-(vecinas +1)*dx,vecinas*dx,Np)\n", " PP[vecinas+1:] = Patm\n", " Particulas_activas = np.array([vecinas,vecinas+1]) # al inicio es solo 2\n", " DT = DT_ini\n", "\n", " \n", " # indice de las particulas en los bordes, al inicio es solo 1\n", " Part_saliente = Particulas_activas[1]\n", " Part_entrante = Particulas_activas[0]\n", " PP[Part_saliente] = Hr*g*rho/2 + Patm" ] }, { "cell_type": "code", "execution_count": 64, "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "dt5BAHCZ9FFV", "outputId": "25f8e37a-8d51-4576-9676-82ad2fb3f479" }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/tmp/ipykernel_31275/1488923836.py:51: NumbaWarning: \n", "Compilation is falling back to object mode WITH looplifting enabled because Function \"DeltaVel\" failed type inference due to: Invalid use of type(CPUDispatcher()) with parameters (float64, array(float64, 1d, C), float64, array(float64, 1d, C), float64, int64, int64)\n", "\n", "During: resolving callee type: type(CPUDispatcher())\n", "During: typing of call at /tmp/ipykernel_31275/1488923836.py (69)\n", "\n", "\n", "File \"../../../tmp/ipykernel_31275/1488923836.py\", line 69:\n", "\n", "\n", " @jit\n", "/tmp/ipykernel_31275/1488923836.py:51: NumbaWarning: \n", "Compilation is falling back to object mode WITHOUT looplifting enabled because Function \"DeltaVel\" failed type inference due to: Cannot determine Numba type of \n", "\n", "File \"../../../tmp/ipykernel_31275/1488923836.py\", line 55:\n", "\n", "\n", " @jit\n", "/home/luis/ambientes/ML/lib/python3.10/site-packages/numba/core/object_mode_passes.py:151: NumbaWarning: Function \"DeltaVel\" was compiled in object mode without forceobj=True, but has lifted loops.\n", "\n", "File \"../../../tmp/ipykernel_31275/1488923836.py\", line 53:\n", "\n", "\n", " warnings.warn(errors.NumbaWarning(warn_msg,\n", "/home/luis/ambientes/ML/lib/python3.10/site-packages/numba/core/object_mode_passes.py:161: NumbaDeprecationWarning: \n", "Fall-back from the nopython compilation path to the object mode compilation path has been detected, this is deprecated behaviour.\n", "\n", "For more information visit https://numba.readthedocs.io/en/stable/reference/deprecation.html#deprecation-of-object-mode-fall-back-behaviour-when-using-jit\n", "\n", "File \"../../../tmp/ipykernel_31275/1488923836.py\", line 53:\n", "\n", "\n", " warnings.warn(errors.NumbaDeprecationWarning(msg,\n", "/tmp/ipykernel_31275/1488923836.py:51: NumbaWarning: \n", "Compilation is falling back to object mode WITHOUT looplifting enabled because Function \"DeltaVel\" failed type inference due to: Invalid use of type(CPUDispatcher()) with parameters (float64, array(float64, 1d, C), float64, array(float64, 1d, C), float64, int64, int64)\n", "\n", "During: resolving callee type: type(CPUDispatcher())\n", "During: typing of call at /tmp/ipykernel_31275/1488923836.py (69)\n", "\n", "\n", "File \"../../../tmp/ipykernel_31275/1488923836.py\", line 69:\n", "\n", "\n", " @jit\n", "/home/luis/ambientes/ML/lib/python3.10/site-packages/numba/core/object_mode_passes.py:151: NumbaWarning: Function \"DeltaVel\" was compiled in object mode without forceobj=True.\n", "\n", "File \"../../../tmp/ipykernel_31275/1488923836.py\", line 55:\n", "\n", "\n", " warnings.warn(errors.NumbaWarning(warn_msg,\n", "/home/luis/ambientes/ML/lib/python3.10/site-packages/numba/core/object_mode_passes.py:161: NumbaDeprecationWarning: \n", "Fall-back from the nopython compilation path to the object mode compilation path has been detected, this is deprecated behaviour.\n", "\n", "For more information visit https://numba.readthedocs.io/en/stable/reference/deprecation.html#deprecation-of-object-mode-fall-back-behaviour-when-using-jit\n", "\n", "File \"../../../tmp/ipykernel_31275/1488923836.py\", line 55:\n", "\n", "\n", " warnings.warn(errors.NumbaDeprecationWarning(msg,\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "============== t = 7.499903536240717e-05 seg. =============\n", "dt : 7.5e-05 Pas.\n", "presion máxima : 3472.7375 Pas.\n", "Vel máxima : 0.003 m/s.\n", "posición del frente: 0.0 m.\n", "# Particulas activas: 2 \n", "============== t = 0.5000343006185202 seg. =============\n", "dt : 7.211e-05 Pas.\n", "presion máxima : 971.3908 Pas.\n", "Vel máxima : 1.624 m/s.\n", "posición del frente: 0.797 m.\n", "# Particulas activas: 27 \n", "============== t = 1.0000019780353664 seg. =============\n", "dt : 7.075e-05 Pas.\n", "presion máxima : 1511.2866 Pas.\n", "Vel máxima : 1.438 m/s.\n", "posición del frente: 1.559 m.\n", "# Particulas activas: 52 \n", "============== t = 1.5000634111258204 seg. =============\n", "dt : 6.969e-05 Pas.\n", "presion máxima : 1861.8675 Pas.\n", "Vel máxima : 1.304 m/s.\n", "posición del frente: 2.242 m.\n", "# Particulas activas: 75 \n", "============== t = 2.0000092189662024 seg. =============\n", "dt : 6.879e-05 Pas.\n", "presion máxima : 2096.564 Pas.\n", "Vel máxima : 1.204 m/s.\n", "posición del frente: 2.867 m.\n", "# Particulas activas: 96 \n", "============== t = 2.5000547225980916 seg. =============\n", "dt : 6.8e-05 Pas.\n", "presion máxima : 2271.1874 Pas.\n", "Vel máxima : 1.125 m/s.\n", "posición del frente: 3.448 m.\n", "# Particulas activas: 115 \n", "============== t = 3.0000626377087896 seg. =============\n", "dt : 6.733e-05 Pas.\n", "presion máxima : 2401.3621 Pas.\n", "Vel máxima : 1.063 m/s.\n", "posición del frente: 3.994 m.\n", "# Particulas activas: 134 \n", "============== t = 3.500044942223491 seg. =============\n", "dt : 6.674e-05 Pas.\n", "presion máxima : 2503.797 Pas.\n", "Vel máxima : 1.011 m/s.\n", "posición del frente: 4.512 m.\n", "# Particulas activas: 151 \n", "============== t = 4.00005290961597 seg. =============\n", "dt : 6.621e-05 Pas.\n", "presion máxima : 2584.5896 Pas.\n", "Vel máxima : 0.968 m/s.\n", "posición del frente: 5.006 m.\n", "# Particulas activas: 167 \n", "============== t = 4.500027056692405 seg. =============\n", "dt : 6.572e-05 Pas.\n", "presion máxima : 2651.4802 Pas.\n", "Vel máxima : 0.931 m/s.\n", "posición del frente: 5.48 m.\n", "# Particulas activas: 183 \n", "============== t = 5.00002102925676 seg. =============\n", "dt : 6.528e-05 Pas.\n", "presion máxima : 2706.678 Pas.\n", "Vel máxima : 0.898 m/s.\n", "posición del frente: 5.937 m.\n", "# Particulas activas: 198 \n", "============== t = 5.500060367799279 seg. =============\n", "dt : 6.486e-05 Pas.\n", "presion máxima : 2755.0256 Pas.\n", "Vel máxima : 0.87 m/s.\n", "posición del frente: 6.379 m.\n", "# Particulas activas: 213 \n", "============== t = 6.000020876002795 seg. =============\n", "dt : 6.451e-05 Pas.\n", "presion máxima : 2795.8142 Pas.\n", "Vel máxima : 0.845 m/s.\n", "posición del frente: 6.72 m.\n", "# Particulas activas: 224 \n", "============== t = 6.5000231351253746 seg. =============\n", "dt : 6.544e-05 Pas.\n", "presion máxima : 2822.3227 Pas.\n", "Vel máxima : 0.828 m/s.\n", "posición del frente: 6.717 m.\n", "# Particulas activas: 224 \n", "tiempo de ejecución: 1092.0246784687042 seg\n" ] } ], "source": [ "inicio = time.time()\n", "print_time = 0\n", "res_x = []\n", "res_P = []\n", "res_V = []\n", "### Loop en el tiempo ### \n", "while tiempo <= Tiempo_total:\n", " #output\n", " if tiempo > print_time:\n", " print (f\"============== t = {tiempo} seg. =============\")\n", " print (f\"dt : {np.round(DT,8)} Pas.\" )\n", " print (f\"presion máxima : {np.round(np.max(PP),4)} Pas.\" )\n", " print (f\"Vel máxima : {np.round(np.max(VV),3)} m/s.\" )\n", " print (f\"posición del frente: {np.round(X_sale,3)} m.\" )\n", " print (f\"# Particulas activas: {len(Particulas_activas)} \" )\n", " #print (f\"aceleracion : {dvatemp[Particulas_activas]}\")\n", " #print (f\"roce:\" , roce)\n", " #print (f\"dvatemp : {dpatemp[Particulas_activas]}\")\n", " print_time += outputTime\n", " res_x.append(XX)\n", " res_P.append(PP)\n", " res_V.append(VV)\n", " ## ================= Pa/dt ============================\n", " dPaa = DeltaPress(Particulas_activas,vecinas,XX,VV,c,mb)\n", " ##rungeKuta 2nd \n", " PP1 = PP - dPaa*DT/2\n", " PP = (PP + PP1 - dPaa*DT)/2\n", " \n", " #print(np.max(PP))\n", " #Updat+\n", " ## ================== Va/dt =============================\n", " dVaa = DeltaVel(Particulas_activas,vecinas,XX,VV,PP,c,mb,theta,D,fric_fac,rho,g)\n", " VV1 = VV - dVaa*DT/2\n", " VV = (VV + VV1 - dVaa*DT)/2\n", " dvatemp = dVaa\n", "\n", " ## corregimos las particulas vecinas ficticias\n", " #en el estanque\n", " Ve = VV[Part_entrante]\n", " Ecine = Ve**2/2/g\n", " VV[XX < XX[Part_entrante]] = Ve\n", " PP[XX <= XX[Part_entrante]] = (Hr - (1+K_loss)*Ecine)*rho*g + Patm\n", " ## hacia la salida\n", " Vs = VV[Part_saliente]\n", " VV[XX>XX[Part_saliente]] = Vs\n", " PP[XX>=XX[Part_saliente]] = Patm\n", "\n", " ##Update Xa\n", " XX = XX + VV*DT\n", "\n", " ## Creamos particulas faltantes y activamos las que correspondan\n", " ### Update las particulas activas\n", " # Particulas nuevas que entran\n", " X_entra = XX[Part_entrante]\n", " X_sale = XX[Part_saliente]\n", "\n", " Pnew = np.flatnonzero((XX < X_entra ) & (XX >= 0))\n", " if len(Pnew) > 0:\n", " #print(X_sale)\n", " X_new_entrante = np.min(XX[Pnew[0]])\n", " ## agregamos particulas ficiticas al arreglo\n", "\n", " Part_fict = len(Pnew) # cantidad de particulas activas en la tub\n", " Xmin = np.min(XX)\n", " XNuevas = np.linspace(Xmin -Part_fict*dx , Xmin, num=Part_fict)\n", " PNuevas = (np.ones_like(XNuevas) * (Hr - Ecine*(1 - K_loss))*rho*g) + Patm\n", " VNuevas = np.zeros_like(XNuevas) + Ve\n", " #print(dPa)\n", " #print(dVa)\n", " XX = np.concatenate((XNuevas,XX), axis=None)\n", " PP = np.concatenate((PNuevas,PP), axis=None)\n", " VV = np.concatenate((VNuevas,VV), axis=None)\n", " \n", "\n", " Part_entrante = np.searchsorted(XX, X_new_entrante, side=\"left\")\n", " Part_saliente = np.searchsorted(XX, X_sale, side=\"left\")\n", " #print(\"la Coordenada de la particula saliente es \",\n", " # np.round(X_sale,4))\n", " \n", " if X_sale <= Ltub:\n", " Particulas_activas = np.flatnonzero((XX>=X_new_entrante) & (XX<=X_sale))\n", "\n", " else:\n", " #print(\"Flujo llega al fin tuberia!\")\n", " #salen particulas para afuera\n", " #identifiquemos las mas alejadas\n", " Psalen = np.flatnonzero((XX > Ltub + vecinas*dx ))\n", " #las sacamos de las matrices\n", " XX = np.delete(XX,Psalen)\n", " PP = np.delete(PP,Psalen)\n", " VV = np.delete(VV,Psalen)\n", " #pasan a ser activas las que estan dentro de los limites\n", " Particulas_activas = np.flatnonzero((XX>=X_new_entrante) & (XX<=Ltub))\n", " Xmax_activo = np.max(XX[Particulas_activas]) \n", " Part_saliente = np.searchsorted(XX, Xmax_activo, side=\"left\")\n", " #finalmente actualizamos los indices de las particulas limites\n", " \n", "\n", " #calculo del dt\n", " Dxx = (XX[1:]-XX[:-1])\n", " Dxx_min = np.min(Dxx)\n", " if Dxx_min < 0 :\n", " print(\"Dx es negativo: error\")\n", " DT = 1e6\n", " else:\n", " DT = Dxx_min/(c+np.max(VV))*courant\n", "\n", " #print(tiempo, DT)\n", "\n", "### loop\n", " tiempo = tiempo + DT\n", "\n", "fin = time.time()\n", "print(\"tiempo de ejecución: \", fin-inicio, \"seg\")" ] }, { "cell_type": "markdown", "metadata": { "id": "yAY5JgySVK2w" }, "source": [ "Notemos que el tiempo de ejecución es igual bastante. (828 segundos), pero esto tomaría más sin numba." ] }, { "cell_type": "code", "execution_count": 65, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 265 }, "id": "oUM-9r5JURrj", "outputId": "e2ef77d3-e4e1-4e97-d795-19e801ef6bf0" }, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "for i in range(len(res_x)):\n", " plt.plot(res_x[i],res_P[i])\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "id": "lilK0qid90n5" }, "source": [ "Adelantando un poco la práctica del método es usual que su aplicación sea en mecánismos de transporte advectivos y eventualmente advectivos - difusivos. Por ejemplo en hidrodinámica, las patículas se discretizan considerando una masa de fluido, la cual es advectada a traves del movimiento de las partículas. Por lo mismo, las distancias entre partículas van a ir variando en cada paso, y no es constante como lo supusimos anteriormente. De este modo, hay que consensuar las siguientes propiedades.\n", "\\begin{equation}\n", "\\rho_i = m_i/V_i\n", "\\end{equation}\n", "donde $\\rho_i$ es la densidad de la partícula i. Es usual suponer al agua como quasicompresible, esto implica que $\\rho_i$ no es constante. En efecto el valor que permanece constante, como ya dijimos, es la masa $m_i$. V es el volumen, que va a depender de las dimensiones n=1,2,3.\n", "De esta manera cuando inicializamos las variables, es usual definir la distancia inicial de las partículas, y obtenemos una estimación inicial del volumen. También inicialmente suponemos que la densidad es constante y por lo tanto estimamos la masa de las partículas. La distancia de la partícula es entonces.\n", "\n", "\\begin{equation}\n", "dr= V^{1/n}\n", "\\end{equation}\n", "\n" ] }, { "cell_type": "markdown", "metadata": { "id": "bGF1TOhSWFkp" }, "source": [ "Finalmente en las PPT quedan expresados los supuestos para la implementación de las ec. de navier-Stokes.\n", "Se recomiendan los siguientes textos de consulta para profundizar." ] }, { "cell_type": "markdown", "metadata": { "id": "UgQBPRTTWVd7" }, "source": [ "## Referencias\n", "\n", "Liu, M. B., & Liu, G. (2010). Smoothed particle hydrodynamics (SPH): an overview and recent developments. Archives of computational methods in engineering, 17(1), 25-76.\n", "\n", "\n", "Monaghan, J. J. (2012). Smoothed particle hydrodynamics and its diverse applications. Annual Review of Fluid Mechanics, 44, 323-346.\n", "\n", "Violeau, D., & Rogers, B. D. (2016). Smoothed particle hydrodynamics (SPH) for free-surface flows: past, present and future. Journal of Hydraulic Research, 54(1), 1-26.\n", "\n", "\n", "### Libros\n", "\n", "Liu, G. R., & Liu, M. B. (2003). Smoothed particle hydrodynamics: a meshfree particle method. World scientific.\n", "\n", "Violeau, D. (2012). Fluid mechanics and the SPH method: theory and applications. Oxford University Press.\n", "\n", "\n", "\n", "## Codigos abiertos recomendados\n", "\n", "https://www.gpusph.org/\n", "\n", "\n", "https://dual.sphysics.org/\n", "\n", "\n", "https://github.com/AndreaAmicarelliRSE/SPHERA\n", "\n", "https://pysph.readthedocs.io/\n", "\n", "\n", "\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "id": "sB6ZrtgXWEgh" }, "outputs": [], "source": [] } ], "metadata": { "colab": { "collapsed_sections": [], "provenance": [] }, "gpuClass": "standard", "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.10.6" } }, "nbformat": 4, "nbformat_minor": 1 }