13-EDP_MOL.ipynb

{
 "cells": [
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Metodo das Linhas\n",
    "\n",
    "O método das linhas é um método semi-discreto para a resolução de EDP's que consiste em discretizar as variáveis espaciais e manter uma das varáveis contínua (usualmente o tempo), de modo a transformar a EDP em um sistema de EDO's que pode então ser\n",
    "resolvido através dos métodos para a resolução de PVI's (como os métodos de Runge-Kutta). A abordagem utilizada para a discretização das variáveis espaciais usualmente é o método de diferenças finitas, por isso o método das linhas é muitas vezes chamado de método de diferenças finitas semi-discreto.\n",
    "\n",
    "Como um exemplo, vamos ver como o método das linhas pode ser utilizado para resolver a equação do calor. A discussão teorica sobre o método das linhas pode ser encontrada no arquivo [em anexo](./assets/material_MOL.pdf). No exemplo resolvido no texto temos a segiunte equação do calor:\n",
    "\n",
    "$$\n",
    "\\frac{\\partial T}{\\partial t} = \\alpha \\frac{\\partial^2 T}{\\partial x^2} - h' \\alpha (T - T_a)\n",
    "$$\n",
    "\n",
    "onde $T$ é a temperatura, $t$ é o tempo, $x$ é a posição, $\\alpha$ é a difusividade térmica, $h'$ é o coeficiente de transferência de calor por convecção e $T_a$ é a temperatura ambiente. \n",
    "\n",
    "<center>\n",
    "<img src=./images/fig_mol.png>\n",
    "</center>\n",
    "\n",
    "As condições de contorno associadas a este problema são:\n",
    "\n",
    "$$\n",
    "T(0,t) = T_{ext} \\\\\n",
    "\\frac{\\partial T}{\\partial x}|_{x=L} = 0\n",
    "$$\n",
    "\n",
    "onde $T_{ext}$ é a temperatura externa e $L$ é o comprimento da barra. As condições iniciais são:\n",
    "\n",
    "$$\n",
    "T(x,0) = T_{ini}\n",
    "$$\n",
    "\n",
    "\n",
    "Neste caso, será considerado um domínio somente com N = 6 pontos para ilustração:\n",
    "\n",
    "<center>\n",
    "<img src=./images/fig_mol1.png>\n",
    "</center>\n",
    "\n",
    "\n",
    "Neste caso, a discretização da EDP na direção x irá resultar um conjunto de valores $(T_1, T_2, T_3, T_4, T_5, T_6)$ que representam a temperatura nos pontos respectivos $(x_1, x_2, x_3, x_4, x_5, x_6)$. Neste caso, porém, estes valores Ti não são constantes, mas podem ser uma função do tempo.\n",
    "\n",
    "Descritizando o dominio espacial, temos:\n",
    "\n",
    "$$\n",
    "\\frac{\\partial^2 T}{\\partial x^2} = \\frac{T_{i-1} - 2T_i + T_{i+1}}{\\Delta x^2}\n",
    "$$\n",
    "\n",
    "subsituindo na equação do calor, temos:\n",
    "\n",
    "$$\n",
    "\\frac{\\partial T_i}{\\partial t} = \\alpha \\frac{T_{i-1} - 2T_i + T_{i+1}}{\\Delta x^2} - h' \\alpha (T_i - T_a)\n",
    "$$\n",
    "\n",
    "Esta equação pode ser aplicada nos pontos i = 2, 3, 4, 5 para obter uma EDO para a temperatura em cada um destes pontos. Para resolver este sistema de EDO's, é preciso definir uma condição inicial para cada ponto. Como a temperatura inicial é considerada\n",
    "constante e igual a Tini, basta associar este valor com a temperatura em cada ponto:\n",
    "\n",
    "$$T_i(0) = T_{ini}$$\n",
    "\n",
    "Para fechar o sistema de equações, é preciso ainda definir equações para $T_0$ e $T_6$, que são obtidas através da aplicação das condições de contorno. A condição $T(0, t) = T_{ext}$ resulta diretamente em:\n",
    "\n",
    "$$T_1 = T_{ext}$$\n",
    "\n",
    "Na extremidade $x = L$, a condição é de derivada nula. Neste caso pode-se aplicar um esquema de discretização para trás, de onde se obtém que $T_6 = T_5$. Com estas duas condições extras, o sistema de EDO's pode ser resolvido.\n",
    "\n",
    "De forma resumida, as equações para os 6 pontos são\n",
    "\n",
    "<center>\n",
    "<img src=./images/fig_mol2.png>\n",
    "</center>\n",
    "\n",
    "Agora vamos implementar este problema no Python. Primeiro, vamos definir as constantes e as condições iniciais:\n",
    "\n",
    "$$\n",
    "\\begin{align}\n",
    "\\alpha &= 0.01 \\; cm^2/s\\\\\n",
    "h' &= 0.1 \\; cm^2\\\\\n",
    "T_a &= 25 \\; C\\\\\n",
    "T_{ini} &= 25 \\; C\\\\\n",
    "T_{ext} &= 100 \\; C\\\\\n",
    "L &= 1 \\; cm\\\\\n",
    "\\Delta x &= \\frac{L}{N-1} \\\\\n",
    "\\Delta t &= 0.01 \\\\\n",
    "\\end{align}\n",
    "$$\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "alpha = 0.01\n",
    "h = 0.1\n",
    "T_a = 25.\n",
    "T_ini = 25.\n",
    "T_ext = 100.\n",
    "L = 1.\n",
    "N = 6\n",
    "dx = L/(N - 1)\n",
    "dt = 0.01\n",
    "\n",
    "duration = 12000\n",
    "t_eval = np.linspace(0, duration, 1000)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Usando o metodo de Euler"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lembrando da implementação do método de Euler para resolver um PVI na forma \n",
    "\n",
    "$$\n",
    "\\frac{dy}{dt} = f(t,y) \\\\\n",
    "$$\n",
    "\n",
    "para fazer um passo $(y_i \\rightarrow y_{i+1})$ temos:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "def euler(func, ti, yi, h=1):\n",
    "    return yi + func(ti, yi) * h"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Agora para usar o método de Euler para resolver o problema de valor inicial, vamos usar a seguinte notação que é mais adequada quando temos um array e estamos no contexto de diferenças finitis:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "alpha = 0.01\n",
    "h = 0.1\n",
    "T_a = 25.\n",
    "T_ini = 25.\n",
    "T_ext = 100.\n",
    "L = 1.\n",
    "N = 6\n",
    "dx = L/(N - 1)\n",
    "dt = 0.01\n",
    "\n",
    "duration = int(120 / dt)\n",
    "t_eval = np.linspace(0, duration, 1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "\n",
    "def _Euler(Tt, h = dt):\n",
    "  \n",
    "    Tt[0] = T_ext\n",
    "    Tt[-1] = Tt[-2]\n",
    "    n = len(Tt) - 1\n",
    "\n",
    "    for i in range(1, n):\n",
    "        Tt[i] = Tt[i] + h*(alpha * (Tt[i + 1] - 2 * Tt[i] + Tt[i - 1]) / dx ** 2 - h * alpha * (Tt[i] - T_a))\n",
    "        \n",
    "        #print(Tt)\n",
    "\n",
    "\n",
    "    Tt[0] =T_ext\n",
    "    Tt[-1] = Tt[-2]\n",
    "\n",
    "    return Tt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "T0 = np.ones(N) * T_ini\n",
    "\n",
    "# boundary conditions\n",
    "T0[0] = T_ext\n",
    "T0[-1] = T0[-2]\n",
    "\n",
    "Tts = [T0.copy()]\n",
    "\n",
    "for _ in range(1, duration):\n",
    "    Tts.append(_Euler(Tts[-1]).copy())\n",
    "\n",
    "Tts = np.array(Tts)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(12000, 6)"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Tts.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "t = np.linspace(0, duration, duration)\n",
    "\n",
    "plt.plot(t, Tts);\n",
    "plt.xlabel('t')\n",
    "plt.ylabel('T');    \n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Py-PDE"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\frac{\\partial T}{\\partial t} = \\alpha \\frac{\\partial^2 T}{\\partial x^2} - h' \\alpha (T - T_a)\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from pde import CartesianGrid, DiffusionPDE, ScalarField\n",
    "import numpy as np\n",
    "import pde"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "alpha = 0.01\n",
    "h = 0.1\n",
    "T_a = 25.0\n",
    "T_ini = 25.0\n",
    "T_ext = 100.0\n",
    "L = 1.0\n",
    "N = 60\n",
    "dt = 0.01\n",
    "\n",
    "duration = 120\n",
    "\n",
    "T0 = np.ones(N) * T_ini # Condições iniciais\n",
    "T0[0] = T_ext # Condições de contorno"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "171c7ef2d95d444a8fa51b9349bd350b",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "  0%|          | 0/120.0 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "grid = CartesianGrid([[0, L]], [N])  # generate grid\n",
    "\n",
    "state = ScalarField(grid, data=T0)  # generate initial condition\n",
    "bc_left = {\"value\": T_ext}  # boundary condition\n",
    "bc_right = {\"derivative\": 0}  # boundary condition\n",
    "bc = [bc_left, bc_right]  # combine boundary conditions\n",
    "eq = pde.PDE({\"T\": \"alpha*laplace(T) - h*alpha*(T - T_a)\"}, \n",
    "             consts={\"alpha\": alpha, \"h\": h, \"T_a\": T_a},\n",
    "             bc=bc)\n",
    "storage = pde.MemoryStorage()\n",
    "result = eq.solve(state, t_range=duration, dt=dt, tracker=[\"progress\", storage.tracker(1)])\n",
    "#result = eq.solve(state, t_range=100, dt=0.001, tracker=[\"plot\", storage.tracker(1)])\n",
    "result.plot();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "2fd9ad09e51742c49314eb652593eefd",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "  0%|          | 0/121 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pde.movie(storage, filename='./outputs/MOL.mp4')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Scipy (Not working)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from scipy.integrate import solve_ivp\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "alpha = 0.01\n",
    "h = 0.1\n",
    "T_a = 25.0\n",
    "T_ini = 25.0\n",
    "T_ext = 100.0\n",
    "L = 1.0\n",
    "N = 10\n",
    "dx = L / (N - 1)\n",
    "dt = 0.01\n",
    "\n",
    "duration = 120\n",
    "t_eval = np.linspace(0, duration, 1000)\n",
    "\n",
    "# Função que representa a EDP\n",
    "def Eq(t, T):\n",
    "    Tt = np.zeros_like(T)\n",
    "    n = len(Tt) - 1\n",
    "    Tt[0] = T_ext\n",
    "    #Tt[-1] = Tt[-2]\n",
    "    \n",
    "    #Tt[1:-1] = alpha * (Tt[2:] - 2 * Tt[1:-1] + Tt[:-2]) / dx ** 2 - h * alpha * (Tt[1:-1] - T_a)\n",
    "    for i in range(1, n):\n",
    "        Tt[i] = alpha * (T[i + 1] - 2 * T[i] + T[i - 1]) / dx ** 2 - h * alpha * (T[i] - T_a)\n",
    "        #alpha * (Tt[i + 1] - 2 * Tt[i] + Tt[i - 1]) / dx ** 2 - h * alpha * (Tt[i] - T_a)\n",
    "    \n",
    "    \n",
    "    # Aplicação das condições de contorno\n",
    "    Tt[0] = T_ext\n",
    "    Tt[-1] = Tt[-2]\n",
    "    print(t, Tt)\n",
    "    \n",
    "    return Tt\n",
    "\n",
    "# Condições iniciais\n",
    "T0 = np.ones(N) * T_ini\n",
    "T0[0] = T_ext\n",
    "\n",
    "print(T0)\n",
    "print(Eq(0, T0))\n",
    "\n",
    "# Resolver a EDP usando solve_ivp\n",
    "res = solve_ivp(Eq, (0, duration), T0, t_eval=t_eval, method='RK45', max_step=0.01)\n",
    "\n",
    "\n",
    "# Plot do resultado\n",
    "\n",
    "plt.figure(figsize=(10, 6))\n",
    "plt.plot(res.t, res.y.T)\n",
    "plt.xlabel('Tempo')\n",
    "plt.ylabel('T')\n",
    "plt.title('Solução da EDP')\n",
    "plt.grid(True)\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(10, 1000)"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res.y.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  100.        ,   112.01201201,   124.02402402, ...,\n",
       "        12075.97597598, 12087.98798799, 12100.        ],\n",
       "       [   25.        ,    32.189396  ,    39.22494523, ...,\n",
       "        11057.05039451, 11068.86123017, 11080.67236109],\n",
       "       [   25.        ,    25.32982404,    26.23233235, ...,\n",
       "        10173.13225177, 10184.75953227, 10196.38739325],\n",
       "       ...,\n",
       "       [   25.        ,    25.        ,    25.00000012, ...,\n",
       "         7687.86383731,  7698.92444025,  7709.98658874],\n",
       "       [   25.        ,    25.        ,    25.        , ...,\n",
       "         7565.19404828,  7576.22456006,  7587.25667189],\n",
       "       [   25.        ,    25.        ,    25.        , ...,\n",
       "         7565.19404828,  7576.22456006,  7587.25667189]])"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res.y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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