ShallowWaterRiemannProblem.ipynb

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      "# Solution of some Riemann problems for the shallow water equations\n",
      "\n",
      "This notebook illustrates the solution to several Riemann problems. In each case an animation shows the evolution of the depth $h(x,t)$ along with a passive tracer (the color of the water) that helps visualize the fluid velocity.  The solution always consists of two waves, each of which might be a shock wave or a rarefaction wave depending on where the left and right states lie in the phase plane.  For each case, a phase plane plot is shown that illustrates how the intermediate state and the nature of each wave can be determined by looking at the intersection of Hugoniot loci and/or integral curves.  This theory is discussed in Chapter 13 of the book \"Finite Volume Methods for Hyperbolic Problems\" and gives more dynamic version of some of the plots in that chapter, see also <http://clawpack.github.io/doc/fvmbook.html>. \n",
      "\n",
      "This notebook can be found in the Clawpack apps repository, see <http://clawpack.github.io/doc/apps.html> for instructions on downloading this repository.  \n",
      "\n",
      "Note that if you download this notebook alone (e.g. from nbviewer), you should be able to run the code that produces the phase plane plots (self-contained in the cells below) but not the cells that run Clawpack (the cells starting with `%%system`) or the cells that produce animations from those results.\n",
      "\n",
      "See <http://clawpack.github.io/doc/notebooks.html> for other Clawpack notebooks."
     ]
    },
    {
     "cell_type": "markdown",
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     "source": [
      "## Contents\n",
      "\n",
      " - <a href=\"#dambreak\">Dam break problem</a>\n",
      " - <a href=\"#twoshock\">Riemann problem for colliding flow (2 shock waves)</a>\n",
      " - <a href=\"#tworare\">Riemann problem for diverging flow (2 rarefaction waves)</a>\n",
      " - <a href=\"#tryit\">Try other states</a>\n"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "First set up various things needed for all the examples:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%pylab inline"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Populating the interactive namespace from numpy and matplotlib\n"
       ]
      }
     ],
     "prompt_number": 67
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Set the CLAW as environment variable before starting notebook, or specify as the second argument to os.environ.get below:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import os, sys\n",
      "CLAW = os.environ.get('CLAW','/Users/rjl/git/clawpack')  \n",
      "sys.path.append(CLAW)  # add to path so clawpack modules can be found\n",
      "os.environ['CLAW'] = CLAW\n",
      "os.environ['PYTHONPATH'] = CLAW  # so Fortran Makefiles work\n",
      "print \"Clawpack directory:  \",CLAW"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Clawpack directory:   /Users/rjl/git/clawpack\n"
       ]
      }
     ],
     "prompt_number": 68
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "example_dir = CLAW + '/apps/notebooks/riemann/shallow'\n",
      "os.chdir(example_dir)\n",
      "print \"Directory where this notebook is located:  \", os.getcwd()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Directory where this notebook is located:   /Users/rjl/git/clawpack/apps/notebooks/riemann/shallow\n"
       ]
      }
     ],
     "prompt_number": 69
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%system\n",
      "make .exe  # Compile the Fortran code and produce executable"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 70,
       "text": [
        "[\"make: Nothing to be done for `.exe'.\"]"
       ]
      }
     ],
     "prompt_number": 70
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import setrun\n",
      "rundata = setrun.setrun()  # initialize most run-time variables for clawpack\n",
      "outdir = '_output'"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 71
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "For making the animations below:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import glob\n",
      "from matplotlib import image\n",
      "from clawpack.visclaw.JSAnimation import IPython_display\n",
      "from matplotlib import animation\n",
      "\n",
      "def init():\n",
      "    im.set_data(image.imread(filenames[0]))\n",
      "    return im,\n",
      "\n",
      "def animate(i):\n",
      "    image_i=image.imread(filenames[i])\n",
      "    im.set_data(image_i)\n",
      "    return im,\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 72
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Set up scripts to plot solution in phase plane $hu$ vs. $h$:"
     ]
    },
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     "cell_type": "code",
     "collapsed": false,
     "input": [
      "g = 1.  # gravitational constant used in book\n",
      "\n",
      "def integral_curve(h, hstar, hustar, wave_family):\n",
      "    \"\"\"Return hu as a function of h for integral curves through (hstar, hustar).\"\"\"\n",
      "    ustar = hustar / hstar\n",
      "    if wave_family == 1:\n",
      "        hu = h*ustar + 2*h*(sqrt(g*hstar) - sqrt(g*h))\n",
      "    else:\n",
      "        hu = h*ustar - 2*h*(sqrt(g*hstar) - sqrt(g*h))\n",
      "    return hu\n",
      "\n",
      "\n",
      "def hugoniot_locus(h, hstar, hustar, wave_family):\n",
      "    \"\"\"Return hu as a function of h for the Hugoniot locus through (hstar, hustar).\"\"\"\n",
      "    ustar = hustar / hstar\n",
      "    alpha = h - hstar\n",
      "    d = sqrt(g*hstar*(1 + alpha/hstar)*(1 + alpha/(2*hstar)))\n",
      "    if wave_family == 1:\n",
      "        hu = hustar + alpha*(ustar - d)\n",
      "    else: \n",
      "        hu = hustar + alpha*(ustar + d)\n",
      "    return hu\n",
      "\n",
      "    \n",
      "def phase_plane_curves(hstar, hustar, state, wave_family='both'):\n",
      "    \"\"\"\n",
      "    Plot the curves of points in the h - hu phase plane that can be connected to (hstar,hustar).\n",
      "    state = 'qleft' or 'qright' indicates whether the specified state is ql or qr. \n",
      "    wave_family = 1, 2, or 'both' indicates whether 1-waves or 2-waves should be plotted.\n",
      "    Colors in the plots indicate whether the states can be connected via a shock or rarefaction.\n",
      "    \"\"\"\n",
      "    \n",
      "    h = linspace(0, hstar, 200)\n",
      "\n",
      "    if wave_family in [1,'both']:\n",
      "        if state == 'qleft':\n",
      "            hu = integral_curve(h, hstar, hustar, 1)\n",
      "            plot(h,hu,'b', label='1-rarefactions')\n",
      "        else:\n",
      "            hu = hugoniot_locus(h, hstar, hustar, 1)\n",
      "            plot(h,hu,'r', label='1-shocks')\n",
      "    \n",
      "    if wave_family in [2,'both']:\n",
      "        if state == 'qleft':\n",
      "            hu = hugoniot_locus(h, hstar, hustar, 2)\n",
      "            plot(h,hu,'g', label='2-shocks')\n",
      "        else:\n",
      "            hu = integral_curve(h, hstar, hustar, 2)\n",
      "            plot(h,hu,'m', label='2-rarefactions')\n",
      "\n",
      "    h = linspace(hstar, 5, 200)\n",
      "\n",
      "    if wave_family in [1,'both']:\n",
      "        if state == 'qright':\n",
      "            hu = integral_curve(h, hstar, hustar, 1)\n",
      "            plot(h,hu,'b', label='1-rarefactions')\n",
      "        else:\n",
      "            hu = hugoniot_locus(h, hstar, hustar, 1)\n",
      "            plot(h,hu,'r', label='1-shocks')\n",
      "    \n",
      "    if wave_family in [2,'both']:\n",
      "        if state == 'qright':\n",
      "            hu = hugoniot_locus(h, hstar, hustar, 2)\n",
      "            plot(h,hu,'g', label='2-shocks')\n",
      "        else:\n",
      "            hu = integral_curve(h, hstar, hustar, 2)\n",
      "            plot(h,hu,'m', label='2-rarefactions')  \n",
      "            \n",
      "    # plot and label the point (hstar, hustar)\n",
      "    plot([hstar],[hustar],'ko',markersize=5)\n",
      "    text(hstar + 0.1, hustar - 0.2, state, fontsize=13)\n",
      "\n",
      "        \n",
      "def make_axes_and_label(x1=-.5, x2=6., y1=-2.5, y2=2.5):\n",
      "    plot([x1,x2],[0,0],'k')\n",
      "    plot([0,0],[y1,y2],'k')\n",
      "    axis([x1,x2,y1,y2])\n",
      "    legend()\n",
      "    xlabel(\"h = depth\",fontsize=15)\n",
      "    ylabel(\"hu = momentum\",fontsize=15)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 73
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     "cell_type": "markdown",
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     "source": [
      "<div id=\"dambreak\"></div>\n",
      "\n",
      "## Dam break Riemann problem:\n",
      "\n",
      "The initial velocity is zero and the depth is greater to the left of $x=0$ than to the right.  The solution is a shock wave moving to the right and a rarefaction wave moving to the left.  The intermediate fluid velocity is positive."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "rundata.probdata.hl = hl = 3.\n",
      "rundata.probdata.ul = ul = 0.\n",
      "rundata.probdata.hr = hr = 1.\n",
      "rundata.probdata.ur = ur = 0.\n",
      "rundata.write()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 74
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%system\n",
      "make output > output.txt\n",
      "make plots > plots.txt"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
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       "prompt_number": 75,
       "text": [
        "['python(36785,0x7fff75847310) malloc: *** error for object 0x100ba1810: pointer being freed was not allocated',\n",
        " '*** set a breakpoint in malloc_error_break to debug',\n",
        " 'make: *** [plots] Abort trap: 6']"
       ]
      }
     ],
     "prompt_number": 75
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      "figno = 1\n",
      "fname = '_plots/*fig' + str(figno) + '.png'\n",
      "filenames=sorted(glob.glob(fname))\n",
      "\n",
      "fig = plt.figure(figsize=(10, 6),dpi=80)\n",
      "ax = fig.add_axes([0, 0, 1, 1])\n",
      "ax.axis('off')\n",
      "im = plt.imshow(image.imread(filenames[0]))\n",
      "\n",
      "\n",
      "animation.FuncAnimation(fig, animate, init_func=init,\n",
      "                              frames=len(filenames), interval=200, blit=True)"
     ],
     "language": "python",
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        "\"></button>\n",
        "    <button onclick=\"anim4573dd1428f68d17.next_frame()\"><img class=\"anim_icon\" src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABQAAAAUCAQAAAAngNWGAAAAAXNSR0IArs4c6QAAAAJiS0dEAP+H\n",
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        "\"></button>\n",
        "    <button onclick=\"anim4573dd1428f68d17.last_frame()\"><img class=\"anim_icon\" src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABQAAAAUCAQAAAAngNWGAAAAAXNSR0IArs4c6QAAAAJiS0dEAP+H\n",
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        "\"></button>\n",
        "    <button onclick=\"anim4573dd1428f68d17.faster()\">+</button>\n",
        "  <form action=\"#n\" name=\"_anim_loop_select4573dd1428f68d17\" class=\"anim_control\">\n",
        "    <input id=\"_frame_no4573dd1428f68d17\" type=\"textbox\" size=\"1\" onchange=\"anim4573dd1428f68d17.set_frame(parseInt(this.value));\" onpaste=\"this.onchange();\" oninput=\"this.onchange();\"></input>\n",
        "    <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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        "    var loop_select_id = \"_anim_loop_select4573dd1428f68d17\";\n",
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        "\"\n",
        "\n",
        "\n",
        "    /* set a timeout to make sure all the above elements are created before\n",
        "       the object is initialized. */\n",
        "    setTimeout(function() {\n",
        "        anim4573dd1428f68d17 = new Animation(frames, img_id, slider_id, frame_id, 200, loop_select_id);\n",
        "    }, 0);\n",
        "  })()\n",
        "</script>\n"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 76,
       "text": [
        "<matplotlib.animation.FuncAnimation at 0x111504290>"
       ]
      }
     ],
     "prompt_number": 76
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "###Phase Plane solution\n",
      "\n",
      "The solution for the dam break problem consists of a 1-rarefaction and a 2-shock.  In the phase plane, the intermediate state is where the 1-wave integral curve from $q_l = (h_l,h_lu_l)$ intersects the 2-wave Hugoniot locus from $q_r = (h_r,h_ru_r)$ "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "phase_plane_curves(hl, hl*ul, state='qleft', wave_family=1)\n",
      "phase_plane_curves(hr, hr*ur, state='qright', wave_family=2)\n",
      "make_axes_and_label()\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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TyYpMlrNnzx5ydXWluLg4ys7OpkGDBpGtrS3VqFGDWrVqRY8fP9bgq1I+Jb3v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\nv7ggMMYYA8AFgTHG2L+4IDDGGAMA/D+hznT0YcI/nwAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x126504a50>"
       ]
      }
     ],
     "prompt_number": 77
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<div id=\"twoshock\"></div>\n",
      "\n",
      "## Symmetric inflow results in two outgoing shock waves\n",
      "\n",
      "The intermediate fluid velocity is zero, so this also flow models a wall at x=0 with flow towards wall:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "rundata.probdata.hl = hl = 2.\n",
      "rundata.probdata.ul = ul = 0.5\n",
      "rundata.probdata.hr = hr = 2.\n",
      "rundata.probdata.ur = ur = -0.5\n",
      "rundata.write()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 78
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%system\n",
      "make output > output.txt\n",
      "make plots > plots.txt"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 79,
       "text": [
        "['python(36821,0x7fff75847310) malloc: *** error for object 0x10183aa10: pointer being freed was not allocated',\n",
        " '*** set a breakpoint in malloc_error_break to debug',\n",
        " 'make: *** [plots] Abort trap: 6']"
       ]
      }
     ],
     "prompt_number": 79
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig = plt.figure(figsize=(10, 6),dpi=80)\n",
      "ax = fig.add_axes([0, 0, 1, 1])\n",
      "ax.axis('off')\n",
      "im = plt.imshow(image.imread(filenames[0]))\n",
      "\n",
      "animation.FuncAnimation(fig, animate, init_func=init,\n",
      "                              frames=len(filenames), interval=200, blit=True)"
     ],
     "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_img5874b30fe1c2ad60\" style=\"width:Nonepx\"> \n",
        "    <br>\n",
        "    <input id=\"_anim_slider5874b30fe1c2ad60\" type=\"range\" style=\"width:350px\" name=\"points\" min=\"0\" max=\"1\" step=\"1\" value=\"0\" onchange=\"anim5874b30fe1c2ad60.set_frame(parseInt(this.value));\"></input>\n",
        "    <br>\n",
        "    <button onclick=\"anim5874b30fe1c2ad60.slower()\">&#8211;</button>\n",
        "    <button onclick=\"anim5874b30fe1c2ad60.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=\"anim5874b30fe1c2ad60.previous_frame()\"><img class=\"anim_icon\" src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABQAAAAUCAQAAAAngNWGAAAAAXNSR0IArs4c6QAAAAJiS0dEAP+H\n",
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        "h8FrxQwtPU99HrwBXsnAwMDAsJiBgYGBoZ1xmKYqALHhMpn1o7igAAAAAElFTkSuQmCC\n",
        "\"></button>\n",
        "    <button onclick=\"anim5874b30fe1c2ad60.reverse_animation()\"><img class=\"anim_icon\" src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABQAAAAUCAQAAAAngNWGAAAAAXNSR0IArs4c6QAAAAJiS0dEAP+H\n",
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        "RK5CYII=\n",
        "\"></button>\n",
        "    <button onclick=\"anim5874b30fe1c2ad60.pause_animation()\"><img class=\"anim_icon\" src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABQAAAAUCAQAAAAngNWGAAAAAXNSR0IArs4c6QAAAAJiS0dEAP+H\n",
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        "AABJRU5ErkJggg==\n",
        "\"></button>\n",
        "    <button onclick=\"anim5874b30fe1c2ad60.play_animation()\"><img class=\"anim_icon\" src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABQAAAAUCAQAAAAngNWGAAAAAXNSR0IArs4c6QAAAAJiS0dEAP+H\n",
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        "Rpcle+Mf8wvgJ16zo/4BtQAAAABJRU5ErkJggg==\n",
        "\"></button>\n",
        "    <button onclick=\"anim5874b30fe1c2ad60.next_frame()\"><img class=\"anim_icon\" src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABQAAAAUCAQAAAAngNWGAAAAAXNSR0IArs4c6QAAAAJiS0dEAP+H\n",
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        "qNIwUMDAwMDAsADKS2NkGL4AAIARMlfNIfZMAAAAAElFTkSuQmCC\n",
        "\"></button>\n",
        "    <button onclick=\"anim5874b30fe1c2ad60.last_frame()\"><img class=\"anim_icon\" src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABQAAAAUCAQAAAAngNWGAAAAAXNSR0IArs4c6QAAAAJiS0dEAP+H\n",
        "j8y/AAAACXBIWXMAAAsTAAALEwEAmpwYAAAAB3RJTUUH3QURCAknOOpFQQAAAS9JREFUKM/dkrEv\n",
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        "FnSONdiL8Qci0lzwpOM5sQAAAABJRU5ErkJggg==\n",
        "\"></button>\n",
        "    <button onclick=\"anim5874b30fe1c2ad60.faster()\">+</button>\n",
        "  <form action=\"#n\" name=\"_anim_loop_select5874b30fe1c2ad60\" class=\"anim_control\">\n",
        "    <input id=\"_frame_no5874b30fe1c2ad60\" type=\"textbox\" size=\"1\" onchange=\"anim5874b30fe1c2ad60.set_frame(parseInt(this.value));\" onpaste=\"this.onchange();\" oninput=\"this.onchange();\"></input>\n",
        "    <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",
        "  /* Instantiate the Animation class. */\n",
        "  /* The IDs given should match those used in the template above. */\n",
        "  (function() {\n",
        "    var img_id = \"_anim_img5874b30fe1c2ad60\";\n",
        "    var slider_id = \"_anim_slider5874b30fe1c2ad60\";\n",
        "    var frame_id = \"_frame_no5874b30fe1c2ad60\"\n",
        "    var loop_select_id = \"_anim_loop_select5874b30fe1c2ad60\";\n",
        "    var frames = new Array(0);\n",
        "    \n",
        "  frames[0] = \"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAtAAAAGwCAYAAACAS1JbAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\\\n",
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        "UpQsTzoGkAAAAABJRU5ErkJggg==\\\n",
        "\"\n",
        "\n",
        "\n",
        "    /* set a timeout to make sure all the above elements are created before\n",
        "       the object is initialized. */\n",
        "    setTimeout(function() {\n",
        "        anim5874b30fe1c2ad60 = new Animation(frames, img_id, slider_id, frame_id, 200, loop_select_id);\n",
        "    }, 0);\n",
        "  })()\n",
        "</script>\n"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 80,
       "text": [
        "<matplotlib.animation.FuncAnimation at 0x122f52cd0>"
       ]
      }
     ],
     "prompt_number": 80
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "###Phase Plane solution\n",
      "\n",
      "The phase plane solution in this case consists of two shock waves and the intermediate state is where the 2-wave Hugoniot locus from $q_l = (h_l,h_lu_l)$ intersects the 1-wave Hugoniot locus from $q_r = (h_r,h_ru_r)$ "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "phase_plane_curves(hl, hl*ul, state='qleft', wave_family=1)\n",
      "phase_plane_curves(hr, hr*ur, state='qright', wave_family=2)\n",
      "make_axes_and_label()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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3bixatAjh4eG4cOGCcsOcrv/qv127di3Cw8Nx+vRpODg4AFAsX52dnY3bt2/D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\nQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x126512150>"
       ]
      }
     ],
     "prompt_number": 81
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<div id=\"tworare\"> </div>\n",
      "\n",
      "##Symmetric outflow giving double rarefaction wave (flow away from wall)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "rundata.probdata.hl = hl = 2.\n",
      "rundata.probdata.ul = ul = -0.5\n",
      "rundata.probdata.hr = hr = 2.\n",
      "rundata.probdata.ur = ur = 0.5\n",
      "rundata.write()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 82
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%system\n",
      "make output > output.txt\n",
      "make plots > plots.txt"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 83,
       "text": [
        "['python(36852,0x7fff75847310) malloc: *** error for object 0x10687c410: pointer being freed was not allocated',\n",
        " '*** set a breakpoint in malloc_error_break to debug',\n",
        " 'make: *** [plots] Abort trap: 6']"
       ]
      }
     ],
     "prompt_number": 83
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig = plt.figure(figsize=(10, 6),dpi=80)\n",
      "ax = fig.add_axes([0, 0, 1, 1])\n",
      "ax.axis('off')\n",
      "im = plt.imshow(image.imread(filenames[0]))\n",
      "\n",
      "animation.FuncAnimation(fig, animate, init_func=init,\n",
      "                              frames=len(filenames), interval=200, blit=True)"
     ],
     "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_imgf933aefce5037301\" style=\"width:Nonepx\"> \n",
        "    <br>\n",
        "    <input id=\"_anim_sliderf933aefce5037301\" type=\"range\" style=\"width:350px\" name=\"points\" min=\"0\" max=\"1\" step=\"1\" value=\"0\" onchange=\"animf933aefce5037301.set_frame(parseInt(this.value));\"></input>\n",
        "    <br>\n",
        "    <button onclick=\"animf933aefce5037301.slower()\">&#8211;</button>\n",
        "    <button onclick=\"animf933aefce5037301.first_frame()\"><img class=\"anim_icon\" src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABQAAAAUCAQAAAAngNWGAAAAAXNSR0IArs4c6QAAAAJiS0dEAP+H\n",
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        "rV+/blxKMZUnLgAAAABJRU5ErkJggg==\n",
        "\"></button>\n",
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        "    <button onclick=\"animf933aefce5037301.faster()\">+</button>\n",
        "  <form action=\"#n\" name=\"_anim_loop_selectf933aefce5037301\" class=\"anim_control\">\n",
        "    <input id=\"_frame_nof933aefce5037301\" type=\"textbox\" size=\"1\" onchange=\"animf933aefce5037301.set_frame(parseInt(this.value));\" onpaste=\"this.onchange();\" oninput=\"this.onchange();\"></input>\n",
        "    <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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