Heat-Equation/.ipynb_checkpoints/main-checkpoint.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 130,
   "metadata": {},
   "outputs": [],
   "source": [
    "#1 Loading functions  and modules\n",
    "from fenics import *\n",
    "import matplotlib.pyplot as plt\n",
    "T = 0.1\n",
    "num_steps = 10\n",
    "dt = T/num_steps\n",
    "rho = 7500\n",
    "Cp = 500\n",
    "k = 50\n",
    "alpha = k/(rho*Cp)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#2 Create mesh and define function space\n",
    "nx = 0.008\n",
    "ny = 0.003\n",
    "mesh = RectangleMesh(Point(0,0),Point(nx,ny),30, 30,'left')\n",
    "V = FunctionSpace(mesh, 'Lagrange', 1) #Lagrange are triangular elements\n",
    "plot(mesh)\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Boundary conditions\n",
    "u0 = Constant(100)\n",
    "def boundary(x, on_boundary):\n",
    "    return on_boundary\n",
    "\n",
    "bc = DirichletBC(V,u0, boundary)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Coefficient(FunctionSpace(Mesh(VectorElement(FiniteElement('Lagrange', triangle, 1), dim=2), 10356), FiniteElement('Lagrange', triangle, 1)), 10369)"
      ]
     },
     "execution_count": 133,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "u_n = project(1, V)\n",
    "u = TrialFunction(V)\n",
    "v = TestFunction(V)\n",
    "f = Constant(0.0)\n",
    "F = u*v*dx + alpha*dt*dot(grad(u), grad(v))*dx-u_n*v*dx\n",
    "a, L = lhs(F), rhs(F)\n",
    "u_n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "u = Function(V)\n",
    "t = 0\n",
    "for n in range(num_steps):\n",
    "    t += dt\n",
    "    #u0.t = t\n",
    "    solve(a == L, u, bc)\n",
    "    c = plot(u,)\n",
    "    plt.colorbar(c)\n",
    "    plt.show()\n",
    "    u_n.assign(u)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.6.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}