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Created January 9, 2014 11:59
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An example showing how to solve the 2D Euler equations in PyClaw, as an IPython notebook.
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"metadata": {
"name": ""
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"worksheets": [
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Two-dimensional compressible fluid dynamics example: Quadrants\n",
"In this example, we solve the Euler equations with initial data consisting of a different state in each quadrant of the unit square. The following block of code will compute the solution at 40 timeframes and should take 1-2 minutes to run."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from clawpack import pyclaw\n",
"from clawpack import riemann\n",
"\n",
"claw = pyclaw.Controller()\n",
"claw.tfinal = 0.6\n",
"claw.num_output_times = 40\n",
"\n",
"riemann_solver = riemann.euler_4wave_2D\n",
"claw.solver = pyclaw.ClawSolver2D(riemann_solver)\n",
"claw.solver.all_bcs = pyclaw.BC.extrap\n",
"\n",
"grid_size = (300,300)\n",
"domain = pyclaw.Domain( (0.,0.), (1.,1.), grid_size)\n",
"\n",
"claw.solution = pyclaw.Solution(claw.solver.num_eqn,domain)\n",
"gam = 1.4\n",
"claw.solution.problem_data['gamma'] = gam\n",
"\n",
"# Set initial data\n",
"q = claw.solution.q\n",
"xx,yy = domain.grid.p_centers\n",
"l = xx<0.5; r = xx>=0.5; b = yy<0.5; t = yy>=0.5\n",
"q[0,...] = 2.*l*t + 1.*l*b + 1.*r*t + 3.*r*b\n",
"q[1,...] = 0.75*t - 0.75*b\n",
"q[2,...] = 0.5*l - 0.5*r\n",
"q[3,...] = 0.5*q[0,...]*(q[1,...]**2+q[2,...]**2) + 1./(gam-1.)\n",
"\n",
"claw.keep_copy = True # Keep solution data in memory for plotting\n",
"claw.output_format = None # Don't write solution data to file\n",
"\n",
"status = claw.run()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"2014-01-09 10:32:47,173 INFO CLAW: Solution 0 computed for time t=0.000000\n"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"2014-01-09 10:32:47,875 INFO CLAW: Solution 1 computed for time t=0.015000\n"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"2014-01-09 10:32:48,594 INFO CLAW: Solution 2 computed for time t=0.030000\n"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"2014-01-09 10:32:49,328 INFO CLAW: Solution 3 computed for time t=0.045000\n"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"2014-01-09 10:32:50,020 INFO CLAW: Solution 4 computed for time t=0.060000\n"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"2014-01-09 10:32:50,720 INFO CLAW: Solution 5 computed for time t=0.075000\n"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"2014-01-09 10:32:51,432 INFO CLAW: Solution 6 computed for time t=0.090000\n"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"2014-01-09 10:32:52,149 INFO CLAW: Solution 7 computed for time t=0.105000\n"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"2014-01-09 10:32:52,879 INFO CLAW: Solution 8 computed for time t=0.120000\n"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"2014-01-09 10:32:53,614 INFO CLAW: Solution 9 computed for time t=0.135000\n"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"2014-01-09 10:32:54,359 INFO CLAW: Solution 10 computed for time t=0.150000\n"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"2014-01-09 10:32:55,115 INFO CLAW: Solution 11 computed for time t=0.165000\n"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"2014-01-09 10:32:55,878 INFO CLAW: Solution 12 computed for time t=0.180000\n"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"2014-01-09 10:32:56,644 INFO CLAW: Solution 13 computed for time t=0.195000\n"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"2014-01-09 10:32:57,414 INFO CLAW: Solution 14 computed for time t=0.210000\n"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"2014-01-09 10:32:58,189 INFO CLAW: Solution 15 computed for time t=0.225000\n"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"2014-01-09 10:32:58,972 INFO CLAW: Solution 16 computed for time t=0.240000\n"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"2014-01-09 10:32:59,764 INFO CLAW: Solution 17 computed for time t=0.255000\n"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"2014-01-09 10:33:00,552 INFO CLAW: Solution 18 computed for time t=0.270000\n"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"2014-01-09 10:33:01,346 INFO CLAW: Solution 19 computed for time t=0.285000\n"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"2014-01-09 10:33:02,136 INFO CLAW: Solution 20 computed for time t=0.300000\n"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"2014-01-09 10:33:02,939 INFO CLAW: Solution 21 computed for time t=0.315000\n"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"2014-01-09 10:33:03,743 INFO CLAW: Solution 22 computed for time t=0.330000\n"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"2014-01-09 10:33:04,551 INFO CLAW: Solution 23 computed for time t=0.345000\n"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"2014-01-09 10:33:05,362 INFO CLAW: Solution 24 computed for time t=0.360000\n"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"2014-01-09 10:33:06,158 INFO CLAW: Solution 25 computed for time t=0.375000\n"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"2014-01-09 10:33:06,959 INFO CLAW: Solution 26 computed for time t=0.390000\n"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"2014-01-09 10:33:07,756 INFO CLAW: Solution 27 computed for time t=0.405000\n"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"2014-01-09 10:33:08,557 INFO CLAW: Solution 28 computed for time t=0.420000\n"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"2014-01-09 10:33:09,369 INFO CLAW: Solution 29 computed for time t=0.435000\n"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"2014-01-09 10:33:10,182 INFO CLAW: Solution 30 computed for time t=0.450000\n"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"2014-01-09 10:33:10,988 INFO CLAW: Solution 31 computed for time t=0.465000\n"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"2014-01-09 10:33:11,793 INFO CLAW: Solution 32 computed for time t=0.480000\n"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"2014-01-09 10:33:12,604 INFO CLAW: Solution 33 computed for time t=0.495000\n"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"2014-01-09 10:33:13,411 INFO CLAW: Solution 34 computed for time t=0.510000\n"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"2014-01-09 10:33:14,225 INFO CLAW: Solution 35 computed for time t=0.525000\n"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"2014-01-09 10:33:15,032 INFO CLAW: Solution 36 computed for time t=0.540000\n"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"2014-01-09 10:33:15,838 INFO CLAW: Solution 37 computed for time t=0.555000\n"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"2014-01-09 10:33:16,643 INFO CLAW: Solution 38 computed for time t=0.570000\n"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"2014-01-09 10:33:17,454 INFO CLAW: Solution 39 computed for time t=0.585000\n"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"2014-01-09 10:33:18,264 INFO CLAW: Solution 40 computed for time t=0.600000\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Plotting: single frame with Matplotlib"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"%pylab inline\n",
"\n",
"frame = claw.frames[40]\n",
"density = frame.q[0,:,:]\n",
"(vx,vy) = np.gradient(density)\n",
"vs = np.sqrt(vx**2 + vy**2)\n",
"x, y = frame.state.grid.c_centers \n",
"\n",
"plt.pcolormesh(x, y, vs, cmap='RdBu')\n",
"plt.axis('image')"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Populating the interactive namespace from numpy and matplotlib\n"
]
},
{
"output_type": "stream",
"stream": "stderr",
"text": [
"WARNING: pylab import has clobbered these variables: ['gamma']\n",
"`%pylab --no-import-all` prevents importing * from pylab and numpy\n"
]
},
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 3,
"text": [
"(0.0016666666666666668,\n",
" 0.99833333333333341,\n",
" 0.0016666666666666668,\n",
" 0.99833333333333341)"
]
},
{
"metadata": {},
"output_type": "display_data",
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DG2+8wcGDBzc1qFah2R+jE+0O65V8GgXX+EbI/TGFfkUkZzuhUOnuI8BOgS81+BmtkWSE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\nRK5CYII=\n",
"text": [
"<matplotlib.figure.Figure at 0x10711c910>"
]
}
],
"prompt_number": 3
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Plotting: animation\n",
"Next we will plot an animation of all 40 frames, using matplotlib and Jake Vanderplas' JSAnimation code."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from matplotlib import animation\n",
"import matplotlib.pyplot as plt\n",
"from clawpack.visclaw.JSAnimation import IPython_display\n",
"import numpy as np\n",
"\n",
"fig = plt.figure(figsize=[4,4])\n",
"\n",
"frame = claw.frames[0]\n",
"density = frame.q[0,:,:]\n",
"(vx,vy) = np.gradient(density)\n",
"vs = np.sqrt(vx**2 + vy**2)\n",
"\n",
"x, y = frame.state.grid.c_centers \n",
"\n",
"# This essentially does a pcolor plot, but it returns the appropriate object\n",
"# for use in animation. See http://matplotlib.org/examples/pylab_examples/pcolor_demo.html.\n",
"# Note that it's necessary to transpose the data array because of the way imshow works.\n",
"im = plt.imshow(vs.T, cmap='Greys', vmin=vs.min(), vmax=vs.max()/20,\n",
" extent=[x.min(), x.max(), y.min(), y.max()],\n",
" interpolation='nearest', origin='lower')\n",
"\n",
"def fplot(frame_number):\n",
" frame = claw.frames[frame_number]\n",
" density = frame.q[0,:,:]\n",
" (vx,vy) = np.gradient(density)\n",
" vs = np.sqrt(vx**2 + vy**2)\n",
" im.set_data(vs.T)\n",
" return im,"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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"text": [
"<matplotlib.figure.Figure at 0x111c14c50>"
]
}
],
"prompt_number": 19
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"animation.FuncAnimation(fig, fplot, frames=len(claw.frames), interval=20)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"html": [
"\n",
"<script language=\"javascript\">\n",
" /* Define the Animation class */\n",
" function Animation(frames, img_id, slider_id, frame_id, interval, loop_select_id){\n",
" this.img_id = img_id;\n",
" this.slider_id = slider_id;\n",
" this.frame_id = frame_id;\n",
" this.loop_select_id = loop_select_id;\n",
" this.interval = interval;\n",
" this.current_frame = 0;\n",
" this.direction = 0;\n",
" this.timer = null;\n",
" this.frames = new Array(frames.length);\n",
"\n",
" for (var i=0; i<frames.length; i++)\n",
" {\n",
" this.frames[i] = new Image();\n",
" this.frames[i].src = frames[i];\n",
" }\n",
" document.getElementById(this.slider_id).max = this.frames.length - 1;\n",
" this.set_frame(this.current_frame);\n",
" }\n",
"\n",
" Animation.prototype.get_loop_state = function(){\n",
" var button_group = document[this.loop_select_id].state;\n",
" for (var i = 0; i < button_group.length; i++) {\n",
" var button = button_group[i];\n",
" if (button.checked) {\n",
" return button.value;\n",
" }\n",
" }\n",
" return undefined;\n",
" }\n",
"\n",
" Animation.prototype.set_frame = function(frame){\n",
" this.current_frame = frame;\n",
" document.getElementById(this.img_id).src = this.frames[this.current_frame].src;\n",
" document.getElementById(this.slider_id).value = this.current_frame;\n",
" document.getElementById(this.frame_id).value = this.current_frame;\n",
" }\n",
"\n",
" Animation.prototype.next_frame = function()\n",
" {\n",
" this.set_frame(Math.min(this.frames.length - 1, this.current_frame + 1));\n",
" }\n",
"\n",
" Animation.prototype.previous_frame = function()\n",
" {\n",
" this.set_frame(Math.max(0, this.current_frame - 1));\n",
" }\n",
"\n",
" Animation.prototype.first_frame = function()\n",
" {\n",
" this.set_frame(0);\n",
" }\n",
"\n",
" Animation.prototype.last_frame = function()\n",
" {\n",
" this.set_frame(this.frames.length - 1);\n",
" } \n",
"\n",
" Animation.prototype.slower = function()\n",
" {\n",
" this.interval /= 0.7;\n",
" if(this.direction > 0){this.play_animation();}\n",
" else if(this.direction < 0){this.reverse_animation();}\n",
" }\n",
"\n",
" Animation.prototype.faster = function()\n",
" {\n",
" this.interval *= 0.7;\n",
" if(this.direction > 0){this.play_animation();}\n",
" else if(this.direction < 0){this.reverse_animation();}\n",
" }\n",
"\n",
" Animation.prototype.anim_step_forward = function()\n",
" {\n",
" this.current_frame += 1;\n",
" if(this.current_frame < this.frames.length){\n",
" this.set_frame(this.current_frame);\n",
" }else{\n",
" var loop_state = this.get_loop_state();\n",
" if(loop_state == \"loop\"){\n",
" this.first_frame();\n",
" }else if(loop_state == \"reflect\"){\n",
" this.last_frame();\n",
" this.reverse_animation();\n",
" }else{\n",
" this.pause_animation();\n",
" this.last_frame();\n",
" }\n",
" }\n",
" }\n",
"\n",
" Animation.prototype.anim_step_reverse = function()\n",
" {\n",
" this.current_frame -= 1;\n",
" if(this.current_frame >= 0){\n",
" this.set_frame(this.current_frame);\n",
" }else{\n",
" var loop_state = this.get_loop_state();\n",
" if(loop_state == \"loop\"){\n",
" this.last_frame();\n",
" }else if(loop_state == \"reflect\"){\n",
" this.first_frame();\n",
" this.play_animation();\n",
" }else{\n",
" this.pause_animation();\n",
" this.first_frame();\n",
" }\n",
" }\n",
" }\n",
"\n",
" Animation.prototype.pause_animation = function()\n",
" {\n",
" this.direction = 0;\n",
" if (this.timer){\n",
" clearInterval(this.timer);\n",
" this.timer = null;\n",
" }\n",
" }\n",
"\n",
" Animation.prototype.play_animation = function()\n",
" {\n",
" this.pause_animation();\n",
" this.direction = 1;\n",
" var t = this;\n",
" if (!this.timer) this.timer = setInterval(function(){t.anim_step_forward();}, this.interval);\n",
" }\n",
"\n",
" Animation.prototype.reverse_animation = function()\n",
" {\n",
" this.pause_animation();\n",
" this.direction = -1;\n",
" var t = this;\n",
" if (!this.timer) this.timer = setInterval(function(){t.anim_step_reverse();}, this.interval);\n",
" }\n",
"</script>\n",
"\n",
"<div class=\"animation\" align=\"center\">\n",
" <img id=\"_anim_imgc5da318c08c35e87\" style=\"width:Nonepx\"> \n",
" <br>\n",
" <input id=\"_anim_sliderc5da318c08c35e87\" type=\"range\" style=\"width:350px\" name=\"points\" min=\"0\" max=\"1\" step=\"1\" value=\"0\" onchange=\"animc5da318c08c35e87.set_frame(parseInt(this.value));\"></input>\n",
" <br>\n",
" <button onclick=\"animc5da318c08c35e87.slower()\">&#8211;</button>\n",
" <button onclick=\"animc5da318c08c35e87.first_frame()\"><img class=\"anim_icon\" src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABQAAAAUCAQAAAAngNWGAAAAAXNSR0IArs4c6QAAAAJiS0dEAP+H\n",
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"rV+/blxKMZUnLgAAAABJRU5ErkJggg==\n",
"\"></button>\n",
" <button onclick=\"animc5da318c08c35e87.previous_frame()\"><img class=\"anim_icon\" src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABQAAAAUCAQAAAAngNWGAAAAAXNSR0IArs4c6QAAAAJiS0dEAP+H\n",
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"\"></button>\n",
" <button onclick=\"animc5da318c08c35e87.reverse_animation()\"><img class=\"anim_icon\" src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABQAAAAUCAQAAAAngNWGAAAAAXNSR0IArs4c6QAAAAJiS0dEAP+H\n",
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"RK5CYII=\n",
"\"></button>\n",
" <button onclick=\"animc5da318c08c35e87.pause_animation()\"><img class=\"anim_icon\" src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABQAAAAUCAQAAAAngNWGAAAAAXNSR0IArs4c6QAAAAJiS0dEAP+H\n",
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"AABJRU5ErkJggg==\n",
"\"></button>\n",
" <button onclick=\"animc5da318c08c35e87.play_animation()\"><img class=\"anim_icon\" src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABQAAAAUCAQAAAAngNWGAAAAAXNSR0IArs4c6QAAAAJiS0dEAP+H\n",
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" <button onclick=\"animc5da318c08c35e87.faster()\">+</button>\n",
" <form action=\"#n\" name=\"_anim_loop_selectc5da318c08c35e87\" class=\"anim_control\">\n",
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" <input type=\"radio\" name=\"state\" value=\"once\" > Once </input>\n",
" <input type=\"radio\" name=\"state\" value=\"loop\" checked> Loop </input>\n",
" <input type=\"radio\" name=\"state\" value=\"reflect\" > Reflect </input>\n",
" </form>\n",
"</div>\n",
"\n",
"\n",
"<script language=\"javascript\">\n",
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" /* The IDs given should match those used in the template above. */\n",
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