ns05.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/latex": [
       "$\\displaystyle - \\frac{2 \\nu \\left(- \\frac{\\left(- 8 t + 2 x\\right) e^{- \\frac{\\left(- 4 t + x\\right)^{2}}{4 \\nu \\left(t + 1\\right)}}}{4 \\nu \\left(t + 1\\right)} - \\frac{\\left(- 8 t + 2 x - 4 \\pi\\right) e^{- \\frac{\\left(- 4 t + x - 2 \\pi\\right)^{2}}{4 \\nu \\left(t + 1\\right)}}}{4 \\nu \\left(t + 1\\right)}\\right)}{e^{- \\frac{\\left(- 4 t + x - 2 \\pi\\right)^{2}}{4 \\nu \\left(t + 1\\right)}} + e^{- \\frac{\\left(- 4 t + x\\right)^{2}}{4 \\nu \\left(t + 1\\right)}}} + 4$"
      ],
      "text/plain": [
       "      ⎛                           2                                         2 \n",
       "      ⎜                -(-4⋅t + x)                         -(-4⋅t + x - 2⋅π)  \n",
       "      ⎜                ─────────────                       ───────────────────\n",
       "      ⎜                 4⋅ν⋅(t + 1)                            4⋅ν⋅(t + 1)    \n",
       "      ⎜  (-8⋅t + 2⋅x)⋅ℯ                (-8⋅t + 2⋅x - 4⋅π)⋅ℯ                   \n",
       "  2⋅ν⋅⎜- ─────────────────────────── - ───────────────────────────────────────\n",
       "      ⎝          4⋅ν⋅(t + 1)                         4⋅ν⋅(t + 1)              \n",
       "- ────────────────────────────────────────────────────────────────────────────\n",
       "                                        2                2                    \n",
       "                       -(-4⋅t + x - 2⋅π)      -(-4⋅t + x)                     \n",
       "                       ───────────────────    ─────────────                   \n",
       "                           4⋅ν⋅(t + 1)         4⋅ν⋅(t + 1)                    \n",
       "                      ℯ                    + ℯ                                \n",
       "\n",
       "⎞    \n",
       "⎟    \n",
       "⎟    \n",
       "⎟    \n",
       "⎟    \n",
       "⎟    \n",
       "⎠    \n",
       "─ + 4\n",
       "     \n",
       "     \n",
       "     \n",
       "     \n",
       "     "
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Burgers' eq\n",
    "\n",
    "\n",
    "\n",
    "import numpy\n",
    "\n",
    "#LATEX\n",
    "#符號計算python庫\n",
    "import sympy\n",
    "\n",
    "from sympy import init_printing\n",
    "from sympy import latex\n",
    "init_printing(use_latex=True)\n",
    "\n",
    "\n",
    "x,nu,t = sympy.symbols('x nu t')\n",
    "#phi = nu*x\n",
    "phi= (sympy.exp(-(x-4*t)**2/ (4*nu*(t+1))) \n",
    "+sympy.exp(-(x-4*t-2*sympy.pi)**2/(4*nu*(t+1))))\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "phiprime = phi.diff(x)\n",
    "\n",
    "#顯示latex程式碼\n",
    "#print(latex(phiprime))\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "from sympy.utilities.lambdify import lambdify\n",
    "\n",
    "u = -2 * nu *(phiprime/phi) +4\n",
    "u\n",
    "\n",
    "\n",
    "#Lambdity: Convert a SymPy expression into a function that allows for fast numeric evaluation.\n",
    "\n",
    "ufunc = lambdify((t,x,nu),u)\n",
    "#print(ufunc(1,4,3))\n",
    "\n",
    "u"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.07798592211502872\n",
      "un: [0.36363636 0.36934835 0.37506034 0.38077232 0.38648431 0.3921963\n",
      " 0.39790828 0.40362027 0.40933226 0.41504424 0.42075623 0.42646822\n",
      " 0.4321802  0.43789219 0.44360418 0.44931616 0.45502815 0.46074014\n",
      " 0.46645212 0.47216411 0.4778761  0.48358808 0.48930007 0.49501206\n",
      " 0.50072404 0.50643603 0.51214802 0.51786    0.52357199 0.52928398\n",
      " 0.53499596 0.54070795 0.54641994 0.55213192 0.55784391 0.5635559\n",
      " 0.56926788 0.57497987 0.58069186 0.58640384 0.59211583 0.59782782\n",
      " 0.6035398  0.60925179 0.61496378 0.62067576 0.62638775 0.63209974\n",
      " 0.63781172 0.64352371 0.6492357  0.65494768 0.66065967 0.66637166\n",
      " 0.67208364 0.67779563 0.68350762 0.6892196  0.69493159 0.70064358\n",
      " 0.70635556 0.71206755 0.71777954 0.72349152 0.72920351 0.7349155\n",
      " 0.74062748 0.74633947 0.75205146 0.75776344 0.76347543 0.76918742\n",
      " 0.7748994  0.78061139 0.78632338 0.79203536 0.79774735 0.80345934\n",
      " 0.80917132 0.81488331 0.8205953  0.82630728 0.83201927 0.83773125\n",
      " 0.84344324 0.84915523 0.85486721 0.8605792  0.86629119 0.87200317\n",
      " 0.87771516 0.88342715 0.88913913 0.89485112 0.90056311 0.90627509\n",
      " 0.91198708 0.91769907 0.92341105 0.92912304 0.93483503]\n",
      "[4.         4.06283185 4.12566371 4.18849556 4.25132741 4.31415927\n",
      " 4.37699112 4.43982297 4.50265482 4.56548668 4.62831853 4.69115038\n",
      " 4.75398224 4.81681409 4.87964594 4.9424778  5.00530965 5.0681415\n",
      " 5.13097336 5.19380521 5.25663706 5.31946891 5.38230077 5.44513262\n",
      " 5.50796447 5.57079633 5.63362818 5.69646003 5.75929189 5.82212374\n",
      " 5.88495559 5.94778745 6.0106193  6.07345115 6.136283   6.19911486\n",
      " 6.26194671 6.32477856 6.38761042 6.45044227 6.51327412 6.57610598\n",
      " 6.63893783 6.70176967 6.76460125 6.82742866 6.89018589 6.95176632\n",
      " 6.99367964 6.72527549 4.         1.27472451 1.00632036 1.04823368\n",
      " 1.10981411 1.17257134 1.23539875 1.29823033 1.36106217 1.42389402\n",
      " 1.48672588 1.54955773 1.61238958 1.67522144 1.73805329 1.80088514\n",
      " 1.863717   1.92654885 1.9893807  2.05221255 2.11504441 2.17787626\n",
      " 2.24070811 2.30353997 2.36637182 2.42920367 2.49203553 2.55486738\n",
      " 2.61769923 2.68053109 2.74336294 2.80619479 2.86902664 2.9318585\n",
      " 2.99469035 3.0575222  3.12035406 3.18318591 3.24601776 3.30884962\n",
      " 3.37168147 3.43451332 3.49734518 3.56017703 3.62300888 3.68584073\n",
      " 3.74867259 3.81150444 3.87433629 3.93716815 4.        ]\n",
      "[3.78645263 3.84593009 3.90540755 3.96488501 4.02436247 4.08383993\n",
      " 4.14331738 4.20279484 4.2622723  4.32174976 4.38122722 4.44070468\n",
      " 4.50018214 4.5596596  4.61913705 4.67861451 4.73809197 4.79756943\n",
      " 4.85704689 4.91652435 4.97600181 5.03547927 5.09495673 5.15443418\n",
      " 5.21391164 5.2733891  5.33286656 5.39234402 5.45182148 5.51129894\n",
      " 5.5707764  5.63025386 5.68973131 5.74920877 5.80868623 5.86816369\n",
      " 5.92764115 5.98711861 6.04659607 6.10607353 6.16555098 6.22502844\n",
      " 6.2845059  6.34398336 6.40346082 6.46293828 6.52241573 6.58189306\n",
      " 6.64136869 6.70081975 6.75991626 6.81390196 6.79524505 5.91949983\n",
      " 2.54326316 1.24494146 1.17899969 1.22958505 1.28844532 1.34788\n",
      " 1.4073545  1.46683175 1.5263092  1.58578665 1.64526411 1.70474157\n",
      " 1.76421903 1.82369649 1.88317395 1.94265141 2.00212887 2.06160632\n",
      " 2.12108378 2.18056124 2.2400387  2.29951616 2.35899362 2.41847108\n",
      " 2.47794854 2.537426   2.59690345 2.65638091 2.71585837 2.77533583\n",
      " 2.83481329 2.89429075 2.95376821 3.01324567 3.07272312 3.13220058\n",
      " 3.19167804 3.2511555  3.31063296 3.37011042 3.42958788 3.48906534\n",
      " 3.5485428  3.60802025 3.66749771 3.72697517 3.78645263]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f3e5c0af0f0>"
      ]
     },
     "execution_count": 114,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1100x700 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib import pyplot \n",
    "%matplotlib inline\n",
    "\n",
    "###variable declaretions\n",
    "nx = 101   #space \n",
    "nt = 100  #time\n",
    "dx = 2 * numpy.pi /(nx -1)\n",
    "sigma = 0.01\n",
    "\n",
    "nu = .07\n",
    "dt = sigma * dx*dx/nu\n",
    "\n",
    "print(nu*nu/dx)\n",
    "\n",
    "x =numpy.linspace(0,2*numpy.pi,nx)\n",
    "\n",
    "un = numpy.empty(nx)\n",
    "print('un:',un )\n",
    "t=0\n",
    "\n",
    "#Initial condition\n",
    "u = numpy.asarray([ufunc(t,x0,nu) for x0 in x])\n",
    "print(u)\n",
    "\n",
    "\n",
    "\n",
    "#periodic boundary condition\n",
    "\n",
    "\n",
    "for n in range(nt):\n",
    "    un = u.copy()\n",
    "    for i in range(1, nx-1):\n",
    "        u[i] = un[i] - un[i] * dt / dx *(un[i] - un[i-1]) + nu * dt / dx**2 *\\\n",
    "                (un[i+1] - 2 * un[i] + un[i-1])\n",
    "    u[0] = un[0] - un[0] * dt / dx * (un[0] - un[-2]) + nu * dt / dx**2 *\\\n",
    "                (un[1] - 2 * un[0] + un[-2])\n",
    "    u[-1] = u[0]\n",
    "\n",
    "u_analytical = numpy.asarray([ufunc(nt*dt, xi, nu) for xi in x])\n",
    "print(u_analytical)\n",
    "    \n",
    "pyplot.figure(figsize=(11, 7), dpi=100)\n",
    "pyplot.plot(x,u, marker='o', lw=2, label='Computational')\n",
    "pyplot.plot(x, u_analytical, label='Analytical')\n",
    "pyplot.xlim([0, 2 * numpy.pi])\n",
    "pyplot.ylim([0, 10])\n",
    "pyplot.legend()\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "'''\n",
    "One of the big differences between Step 4 and the previous lessons \n",
    "is the use of periodic boundary conditions. \n",
    "If you experiment with Steps 1 and 2 and make the simulation run longer (by increasing nt) \n",
    "you will notice that the wave will keep moving to the right until it no longer even shows up\n",
    "in the plot.\n",
    "'''"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import webbrowser\n",
    "webbrowser.open(\"https://en.wikipedia.org/wiki/Burgers'_equation\")"
   ]
  }
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