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{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 2D Euler Quadrants with PyClaw\n",
"## Aron Ahmadia\n",
"\n",
"This entire notebook is licensed under a Creative Commons Attribution 3.0 Unported License.\n",
"\n",
"All code in this notebook is usable under the terms of the BSD license.\n",
"\n",
"![\"Creative](\"http://i.creativecommons.org/l/by/3.0/88x31.png\"/)
\n",
"\n",
"This example demonstrates the interactive properties of PyClaw from a web notebook.\n",
"\n",
"The data here consists of four constant values in four quadrants chosen so that each pair of data gives a single shock wave in its solution. The interaction at the corner leads to a more complicated wave structure. \n",
"\n",
"The four fields are:\n",
"\n",
"* density\n",
"* momentum in $u$\n",
"* momentum in $v$\n",
"* energy\n",
"\n",
"For more information, see:\n",
"\n",
"Figure 4 of C. W. Schulz-Rinne and J. P. Collins and H. M. Glaz, Numerical Solution of the {R}iemann Problem for Two-Dimensional Gas Dynamics, SIAM J. Sci. Comput. 14 (1993), pp. 1394-1414\n",
"\n",
"Figure 6 in R. J. LeVeque, Wave propagation algorithms for multi-dimensional hyperbolic systems, J. Comput. Phys. 131 (1997), pp. 327-353."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"%matplotlib inline\n",
"import matplotlib.pyplot as plt\n",
"from matplotlib import animation\n",
"import numpy as np\n",
"plt.rcParams['figure.figsize'] = 10, 10"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 54
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#!/usr/bin/env python\n",
"# encoding: utf-8\n",
"\n",
"\"\"\"\n",
"Solve the Euler equations of compressible fluid dynamics.\n",
"\"\"\"\n",
"from clawpack import pyclaw\n",
"from clawpack import riemann\n",
"\n",
"Nx=200\n",
"Ny=200\n",
"\n",
"solver = pyclaw.ClawSolver2D(riemann.euler_4wave_2D)\n",
"solver.all_bcs = pyclaw.BC.extrap\n",
"\n",
"domain = pyclaw.Domain([0.,0.],[1.,1.],[Nx,Ny])\n",
"solution = pyclaw.Solution(solver.num_eqn,domain)\n",
"gamma = 1.4\n",
"solution.problem_data['gamma'] = gamma\n",
"solver.dimensional_split = False\n",
"solver.transverse_waves = 2"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 55
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Set initial data\n",
"xx,yy = domain.grid.p_centers\n",
"l = xx<0.8; r = xx>=0.8; b = yy<0.8; t = yy>=0.8\n",
"solution.q[0,...] = 1.5*r*t + 0.532258064516129*l*t + 0.137992831541219*l*b + 0.532258064516129*r*b\n",
"u = 0.*r*t + 1.206045378311055*l*t + 1.206045378311055*l*b + 0.*r*b\n",
"v = 0.*r*t + 0.*l*t + 1.206045378311055*l*b + 1.206045378311055*r*b\n",
"p = 1.5*r*t + 0.3*l*t + 0.029032258064516*l*b + 0.3*r*b\n",
"solution.q[1,...] = solution.q[0,...] * u\n",
"solution.q[2,...] = solution.q[0,...] * v\n",
"solution.q[3,...] = 0.5*solution.q[0,...]*(u**2+v**2) + p/(gamma-1.)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 56
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def display_q(q):\n",
" x = np.linspace(0, 1, Nx)\n",
" y = np.linspace(0, 1, Ny)\n",
" x,y = np.meshgrid(x,y)\n",
" z = q[0,:,:]\n",
" cont = ax.contourf(x, y, z, 500)\n",
" return cont"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 57
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"fig = plt.figure()\n",
"ax = plt.axes(xlim=(0, 1), ylim=(0, 1))\n",
"display_q(solution.q)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 58,
"text": [
""
]
},
{
"metadata": {},
"output_type": "display_data",
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"text": [
""
]
}
],
"prompt_number": 58
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"claw = pyclaw.Controller()\n",
"claw.keep_copy=True\n",
"claw.tfinal = 0.8\n",
"claw.num_output_times = 10\n",
"claw.solution = solution\n",
"claw.solver = solver"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 59
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"status = claw.run()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"2013-11-17 13:09:37,950 INFO CLAW: Solution 0 computed for time t=0.000000\n"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"2013-11-17 13:09:39,615 INFO CLAW: Solution 1 computed for time t=0.080000\n"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"2013-11-17 13:09:41,297 INFO CLAW: Solution 2 computed for time t=0.160000\n"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"2013-11-17 13:09:43,090 INFO CLAW: Solution 3 computed for time t=0.240000\n"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"2013-11-17 13:09:44,874 INFO CLAW: Solution 4 computed for time t=0.320000\n"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"2013-11-17 13:09:46,675 INFO CLAW: Solution 5 computed for time t=0.400000\n"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"2013-11-17 13:09:48,523 INFO CLAW: Solution 6 computed for time t=0.480000\n"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"2013-11-17 13:09:50,389 INFO CLAW: Solution 7 computed for time t=0.560000\n"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"2013-11-17 13:09:52,302 INFO CLAW: Solution 8 computed for time t=0.640000\n"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"2013-11-17 13:09:54,295 INFO CLAW: Solution 9 computed for time t=0.720000\n"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"2013-11-17 13:09:56,310 INFO CLAW: Solution 10 computed for time t=0.800000\n"
]
}
],
"prompt_number": 60
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"VIDEO_TAG = \"\"\"\"\"\"\n",
"\n",
"def anim_to_html(anim):\n",
" if not hasattr(anim, '_encoded_video'):\n",
" with open('animation.mp4','w') as f:\n",
" anim.save(f.name, fps=1, extra_args=['-vcodec', 'libx264'])\n",
" video = open(f.name, \"rb\").read()\n",
" anim._encoded_video = video.encode(\"base64\")\n",
" \n",
" return VIDEO_TAG.format(anim._encoded_video)\n",
"\n",
"from IPython.display import HTML\n",
"\n",
"def display_animation(anim):\n",
" plt.close(anim._fig)\n",
" return HTML(anim_to_html(anim))"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 61
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"fig = plt.figure()\n",
"ax = plt.axes(xlim=(0, 1), ylim=(0, 1))\n",
"\n",
"def animate(i): \n",
" display_q(claw.frames[i].q)\n",
" \n",
"anim = animation.FuncAnimation(fig, animate, frames=len(claw.frames), blit=False)\n",
"print \"created animation\"\n",
"display_animation(anim)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"created animation\n"
]
},
{
"html": [
""
],
"metadata": {},
"output_type": "pyout",
"prompt_number": 62,
"text": [
""
]
}
],
"prompt_number": 62
},
{
"cell_type": "code",
"collapsed": false,
"input": [],
"language": "python",
"metadata": {},
"outputs": []
}
],
"metadata": {}
}
]
}