Convection_FD.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[    0.     0.     0.     0.     0.     0.     0.     0.     0.     0.]\n",
      " [    0.  1062.   -81.     0.     0.     0.     0.     0.     0.     0.]\n",
      " [    0.  -981.  1062.   -81.     0.     0.     0.     0.     0.     0.]\n",
      " [    0.     0.  -981.  1062.   -81.     0.     0.     0.     0.     0.]\n",
      " [    0.     0.     0.  -981.  1062.   -81.     0.     0.     0.     0.]\n",
      " [    0.     0.     0.     0.  -981.  1062.   -81.     0.     0.     0.]\n",
      " [    0.     0.     0.     0.     0.  -981.  1062.   -81.     0.     0.]\n",
      " [    0.     0.     0.     0.     0.     0.  -981.  1062.   -81.     0.]\n",
      " [    0.     0.     0.     0.     0.     0.     0.  -981.  1062.     0.]\n",
      " [    0.     0.     0.     0.     0.     0.     0.     0.     0.     0.]]\n"
     ]
    },
    {
     "data": {
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Laaq6jOY3/ZbXFrR4rMAct3Wd6zZEFKbWFx0ia3Euh47WMW/6RVw/0r5CYoxb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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10e6a69e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "def conv_cent(A,grid,conv=100):\n",
    "    for i in range(1,grid.size-1):\n",
    "        h=grid[i+1]-grid[i-1]\n",
    "        if i==1:\n",
    "            A[i,i+1]+=conv/h\n",
    "        elif i==grid.size-2:\n",
    "            A[i,i-1]+=-conv/h\n",
    "        else:\n",
    "            A[i,i+1]+=conv/h\n",
    "            A[i,i-1]+=-conv/h\n",
    "    return A\n",
    "\n",
    "def conv_upwind(A,grid,conv=100):\n",
    "    for i in range(1,grid.size-1):\n",
    "        if conv>0:\n",
    "            h=grid[i]-grid[i-1]\n",
    "            A[i,i]+=conv/h\n",
    "            if i>1:\n",
    "                A[i,i-1]+=-conv/h\n",
    "        else:\n",
    "            h=grid[i+1]-grid[i]\n",
    "            A[i,i]-=conv/h\n",
    "            if i<grid.size-2:\n",
    "                A[i,i+1]+=conv/h\n",
    "    return A\n",
    "                \n",
    "\n",
    "def diff_cent(A,grid,diff=1):\n",
    "    for i in range(1,grid.size-1):\n",
    "        hr=grid[i+1]-grid[i]\n",
    "        hl=grid[i]-grid[i-1]\n",
    "        denom=1/(hl*hr*(hl+hr))\n",
    "        if i==1:\n",
    "            A[i,i+1]-=2*hl*diff*denom\n",
    "        elif i==grid.size-2:\n",
    "            A[i,i-1]-=2*hr*diff*denom\n",
    "        else:\n",
    "            A[i,i+1]-=2*hl*diff*denom\n",
    "            A[i,i-1]-=2*hr*diff*denom\n",
    "        A[i,i]+=2*(hl+hr*diff)*denom\n",
    "    return A\n",
    "\n",
    "\n",
    "\n",
    "grid=np.linspace(0,1,10)\n",
    "A=np.zeros((grid.size,grid.size))\n",
    "A=diff_cent(A,grid)\n",
    "A=conv_upwind(A,grid)\n",
    "print(A)\n",
    "u=np.zeros(grid.size)\n",
    "b=np.ones(grid.size)\n",
    "u[1:-1]=np.linalg.solve(A[1:-1,1:-1],b[1:-1])\n",
    "plt.plot(grid,u)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Wo2i1jqIx1rzFeErLNh6dn5m0bP0ehlSUcPLoIR2WMTPmTK/m2fqd7OvC8JaISL6ECRTL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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1135d4358>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0.          0.01234568  0.02138334  0.03703704  0.06415003  0.11111111\n",
      "  0.19245009  0.33333333  0.57735027  1.        ]\n"
     ]
    }
   ],
   "source": [
    "n=9\n",
    "grid=np.geomspace(1/n**2,1,n)\n",
    "grid=np.hstack((0,grid))\n",
    "A=np.zeros((grid.size,grid.size))\n",
    "A=diff_cent(A,grid)\n",
    "A=conv_cent(A,grid,-1000)\n",
    "#print(A)\n",
    "u=np.zeros(grid.size)\n",
    "b=np.ones(grid.size)\n",
    "u[1:-1]=np.linalg.solve(A[1:-1,1:-1],b[1:-1])\n",
    "plt.plot(grid,u)\n",
    "plt.show()\n",
    "print(grid)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python [conda root]",
   "language": "python",
   "name": "conda-root-py"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}