There are two different forms of Richards equation that differ on how they deal with the non-linearity in the time-stepping term. Here we reproduce results from a seminal paper, and show the ease with which you can do this in SimPEG and Richards python packages.
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Richards Equation - Comparison to Ceilia et al. 1990
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| <p><strong>Objective:</strong></p> | |
| <p>There are two different forms of Richards equation that differ | |
| on how they deal with the non-linearity in the time-stepping term.</p> | |
| <p>The most fundamental form, referred to as the | |
| 'mixed'-form of Richards Equation [Celia <em>et al.</em>, 1990]</p> | |
| <p>$$\frac{\partial \theta(\psi)}{\partial t} - \nabla \cdot k(\psi) \nabla \psi - \frac{\partial k(\psi)}{\partial z} = 0 | |
| \quad \psi \in \Omega$$</p> | |
| <p>where $\theta$ is water content, and $\psi$ is pressure head. | |
| This formulation of Richards equation is called the | |
| 'mixed'-form because the equation is parameterized in $\psi$ | |
| but the time-stepping is in terms of $\theta$.</p> | |
| <p>As noted in [Celia <em>et al.</em>, 1990] the 'head'-based form of Richards | |
| equation can be written in the continuous form as:</p> | |
| <p>$$\frac{\partial \theta}{\partial \psi}\frac{\partial \psi}{\partial t} - \nabla \cdot k(\psi) \nabla \psi - \frac{\partial k(\psi)}{\partial z} = 0 \quad \psi \in \Omega$$</p> | |
| <p>However, it can be shown that this does not conserve mass in the discrete formulation.</p> | |
| <p>Here we reproduce the results from Ceilia <em>et al.</em> (1990) demonstrating that the head-based formulation is not as good as the mixed-formulation.</p> | |
| <p><em>Celia, Michael A., Efthimios T. Bouloutas, and Rebecca L. Zarba. "<a href="http://www.webpages.uidaho.edu/ch/papers/Celia.pdf">A general mass-conservative numerical solution for the unsaturated flow equation.</a>" Water Resources Research 26.7 (1990): 1483-1496.</em></p> | |
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| In [1]: | |
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| <div class="highlight"><pre><span class="kn">from</span> <span class="nn">SimPEG</span> <span class="kn">import</span> <span class="o">*</span> | |
| <span class="kn">import</span> <span class="nn">Richards</span> | |
| </pre></div> | |
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| <pre> | |
| Warning: mumps solver not available. | |
| </pre> | |
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| <div class="highlight"><pre><span class="n">M</span> <span class="o">=</span> <span class="n">mesh</span><span class="o">.</span><span class="n">TensorMesh</span><span class="p">([</span><span class="n">np</span><span class="o">.</span><span class="n">ones</span><span class="p">(</span><span class="mi">40</span><span class="p">)])</span> | |
| <span class="n">M</span><span class="o">.</span><span class="n">setCellGradBC</span><span class="p">(</span><span class="s">'dirichlet'</span><span class="p">)</span> | |
| <span class="n">Ks</span> <span class="o">=</span> <span class="mf">9.4400e-03</span> | |
| <span class="n">E</span> <span class="o">=</span> <span class="n">Richards</span><span class="o">.</span><span class="n">Haverkamp</span><span class="p">(</span><span class="n">Ks</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">log</span><span class="p">(</span><span class="n">Ks</span><span class="p">),</span> <span class="n">A</span><span class="o">=</span><span class="mf">1.1750e+06</span><span class="p">,</span> <span class="n">gamma</span><span class="o">=</span><span class="mf">4.74</span><span class="p">,</span> | |
| <span class="n">alpha</span><span class="o">=</span><span class="mf">1.6110e+06</span><span class="p">,</span> <span class="n">theta_s</span><span class="o">=</span><span class="mf">0.287</span><span class="p">,</span> | |
| <span class="n">theta_r</span><span class="o">=</span><span class="mf">0.075</span><span class="p">,</span> <span class="n">beta</span><span class="o">=</span><span class="mf">3.96</span><span class="p">)</span> | |
| <span class="n">bc</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="o">-</span><span class="mf">61.5</span><span class="p">,</span><span class="o">-</span><span class="mf">20.7</span><span class="p">])</span> | |
| <span class="n">h</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="n">M</span><span class="o">.</span><span class="n">nC</span><span class="p">)</span> <span class="o">+</span> <span class="n">bc</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> | |
| <span class="k">def</span> <span class="nf">getFields</span><span class="p">(</span><span class="n">timeStep</span><span class="p">,</span><span class="n">method</span><span class="p">):</span> | |
| <span class="n">prob</span> <span class="o">=</span> <span class="n">Richards</span><span class="o">.</span><span class="n">RichardsProblem</span><span class="p">(</span><span class="n">M</span><span class="p">,</span><span class="n">E</span><span class="p">,</span> <span class="n">timeStep</span><span class="o">=</span><span class="n">timeStep</span><span class="p">,</span> <span class="n">timeEnd</span><span class="o">=</span><span class="mi">360</span><span class="p">,</span> | |
| <span class="n">boundaryConditions</span><span class="o">=</span><span class="n">bc</span><span class="p">,</span> <span class="n">initialConditions</span><span class="o">=</span><span class="n">h</span><span class="p">,</span> | |
| <span class="n">doNewton</span><span class="o">=</span><span class="bp">False</span><span class="p">,</span> <span class="n">method</span><span class="o">=</span><span class="n">method</span><span class="p">)</span> | |
| <span class="k">return</span> <span class="n">prob</span><span class="o">.</span><span class="n">field</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">log</span><span class="p">(</span><span class="n">Ks</span><span class="p">))</span> | |
| <span class="n">Hs_M10</span> <span class="o">=</span> <span class="n">getFields</span><span class="p">(</span><span class="mi">10</span><span class="p">,</span> <span class="s">'mixed'</span><span class="p">)</span> | |
| <span class="n">Hs_M30</span> <span class="o">=</span> <span class="n">getFields</span><span class="p">(</span><span class="mi">30</span><span class="p">,</span> <span class="s">'mixed'</span><span class="p">)</span> | |
| <span class="n">Hs_M120</span><span class="o">=</span> <span class="n">getFields</span><span class="p">(</span><span class="mi">120</span><span class="p">,</span><span class="s">'mixed'</span><span class="p">)</span> | |
| <span class="n">Hs_H10</span> <span class="o">=</span> <span class="n">getFields</span><span class="p">(</span><span class="mi">10</span><span class="p">,</span> <span class="s">'head'</span><span class="p">)</span> | |
| <span class="n">Hs_H30</span> <span class="o">=</span> <span class="n">getFields</span><span class="p">(</span><span class="mi">30</span><span class="p">,</span> <span class="s">'head'</span><span class="p">)</span> | |
| <span class="n">Hs_H120</span><span class="o">=</span> <span class="n">getFields</span><span class="p">(</span><span class="mi">120</span><span class="p">,</span><span class="s">'head'</span><span class="p">)</span> | |
| </pre></div> | |
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| <pre> | |
| NewtonRoot stopped by maxIters. norm: 5.1942e-05 | |
| NewtonRoot stopped by maxIters. norm: 1.0531e-06 | |
| NewtonRoot stopped by maxIters. norm: 1.1545e-06 | |
| NewtonRoot stopped by maxIters. norm: 2.2226e-06 | |
| NewtonRoot stopped by maxIters. norm: 2.6211e-06 | |
| </pre> | |
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| <div class="highlight"><pre><span class="n">figure</span><span class="p">(</span><span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">13</span><span class="p">,</span><span class="mi">5</span><span class="p">))</span> | |
| <span class="n">subplot</span><span class="p">(</span><span class="mi">121</span><span class="p">)</span> | |
| <span class="n">plot</span><span class="p">(</span><span class="mi">40</span><span class="o">-</span><span class="n">M</span><span class="o">.</span><span class="n">gridCC</span><span class="p">,</span> <span class="n">Hs_M10</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">],</span><span class="s">'b-'</span><span class="p">)</span> | |
| <span class="n">plot</span><span class="p">(</span><span class="mi">40</span><span class="o">-</span><span class="n">M</span><span class="o">.</span><span class="n">gridCC</span><span class="p">,</span> <span class="n">Hs_M30</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">],</span><span class="s">'r-'</span><span class="p">)</span> | |
| <span class="n">plot</span><span class="p">(</span><span class="mi">40</span><span class="o">-</span><span class="n">M</span><span class="o">.</span><span class="n">gridCC</span><span class="p">,</span> <span class="n">Hs_M120</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">],</span><span class="s">'k-'</span><span class="p">)</span> | |
| <span class="n">title</span><span class="p">(</span><span class="s">'Mixed Method'</span><span class="p">);</span><span class="n">xlabel</span><span class="p">(</span><span class="s">'Depth, cm'</span><span class="p">);</span><span class="n">ylabel</span><span class="p">(</span><span class="s">'Pressure Head, cm'</span><span class="p">)</span> | |
| <span class="n">legend</span><span class="p">((</span><span class="s">'dt = 10 sec'</span><span class="p">,</span><span class="s">'dt = 30 sec'</span><span class="p">,</span><span class="s">'dt = 120 sec'</span><span class="p">))</span> | |
| <span class="n">subplot</span><span class="p">(</span><span class="mi">122</span><span class="p">)</span> | |
| <span class="n">plot</span><span class="p">(</span><span class="mi">40</span><span class="o">-</span><span class="n">M</span><span class="o">.</span><span class="n">gridCC</span><span class="p">,</span> <span class="n">Hs_H10</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">],</span><span class="s">'b-'</span><span class="p">)</span> | |
| <span class="n">plot</span><span class="p">(</span><span class="mi">40</span><span class="o">-</span><span class="n">M</span><span class="o">.</span><span class="n">gridCC</span><span class="p">,</span> <span class="n">Hs_H30</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">],</span><span class="s">'r-'</span><span class="p">)</span> | |
| <span class="n">plot</span><span class="p">(</span><span class="mi">40</span><span class="o">-</span><span class="n">M</span><span class="o">.</span><span class="n">gridCC</span><span class="p">,</span> <span class="n">Hs_H120</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">],</span><span class="s">'k-'</span><span class="p">)</span> | |
| <span class="n">title</span><span class="p">(</span><span class="s">'Head-Based Method'</span><span class="p">);</span><span class="n">xlabel</span><span class="p">(</span><span class="s">'Depth, cm'</span><span class="p">);</span><span class="n">ylabel</span><span class="p">(</span><span class="s">'Pressure Head, cm'</span><span class="p">)</span> | |
| <span class="n">legend</span><span class="p">((</span><span class="s">'dt = 10 sec'</span><span class="p">,</span><span class="s">'dt = 30 sec'</span><span class="p">,</span><span class="s">'dt = 120 sec'</span><span class="p">))</span> | |
| </pre></div> | |
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| <pre> | |
| <matplotlib.legend.Legend at 0x10fb352d0> | |
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| In [4]: | |
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| <div class="highlight"><pre><span class="k">def</span> <span class="nf">function</span><span class="p">(</span><span class="n">var</span><span class="p">,</span> <span class="n">ax</span><span class="p">,</span> <span class="n">clim</span><span class="p">,</span> <span class="n">tlt</span><span class="p">,</span> <span class="n">i</span><span class="p">):</span> | |
| <span class="n">ax</span><span class="o">.</span><span class="n">cla</span><span class="p">()</span> | |
| <span class="n">linem</span><span class="p">,</span> <span class="o">=</span> <span class="n">ax</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="mi">40</span><span class="o">-</span><span class="n">M</span><span class="o">.</span><span class="n">gridCC</span><span class="p">,</span> <span class="n">Hs_M10</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="s">'r-'</span><span class="p">,</span> <span class="n">lw</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span> | |
| <span class="n">lineh</span><span class="p">,</span> <span class="o">=</span> <span class="n">ax</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="mi">40</span><span class="o">-</span><span class="n">M</span><span class="o">.</span><span class="n">gridCC</span><span class="p">,</span> <span class="n">Hs_H10</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="s">'b-'</span><span class="p">,</span> <span class="n">lw</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span> | |
| <span class="n">ax</span><span class="o">.</span><span class="n">legend</span><span class="p">((</span><span class="s">'mixed'</span><span class="p">,</span><span class="s">'head'</span><span class="p">))</span> | |
| <span class="n">ax</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="s">'Time %4.f seconds'</span><span class="o">%</span><span class="p">(</span><span class="n">i</span><span class="o">*</span><span class="mi">10</span><span class="p">))</span> | |
| <span class="n">M</span><span class="o">.</span><span class="n">video</span><span class="p">(</span><span class="n">Hs_H10</span><span class="p">,</span><span class="n">function</span><span class="p">,</span><span class="n">colorbar</span><span class="o">=</span><span class="bp">False</span><span class="p">,</span><span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">6</span><span class="p">,</span><span class="mi">5</span><span class="p">))</span> | |
| </pre></div> | |
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| Out[4]:</div> | |
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| </div> |
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| { | |
| "metadata": { | |
| "name": "" | |
| }, | |
| "nbformat": 3, | |
| "nbformat_minor": 0, | |
| "worksheets": [ | |
| { | |
| "cells": [ | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "**Objective:**\n", | |
| "\n", | |
| "There are two different forms of Richards equation that differ\n", | |
| "on how they deal with the non-linearity in the time-stepping term.\n", | |
| "\n", | |
| "The most fundamental form, referred to as the\n", | |
| "'mixed'-form of Richards Equation [Celia *et al.*, 1990]\n", | |
| "\n", | |
| "$$\\frac{\\partial \\theta(\\psi)}{\\partial t} - \\nabla \\cdot k(\\psi) \\nabla \\psi - \\frac{\\partial k(\\psi)}{\\partial z} = 0\n", | |
| "\\quad \\psi \\in \\Omega$$\n", | |
| "\n", | |
| "where $\\theta$ is water content, and $\\psi$ is pressure head.\n", | |
| "This formulation of Richards equation is called the\n", | |
| "'mixed'-form because the equation is parameterized in $\\psi$\n", | |
| "but the time-stepping is in terms of $\\theta$.\n", | |
| "\n", | |
| "As noted in [Celia *et al.*, 1990] the 'head'-based form of Richards\n", | |
| "equation can be written in the continuous form as:\n", | |
| "\n", | |
| "$$\\frac{\\partial \\theta}{\\partial \\psi}\\frac{\\partial \\psi}{\\partial t} - \\nabla \\cdot k(\\psi) \\nabla \\psi - \\frac{\\partial k(\\psi)}{\\partial z} = 0 \\quad \\psi \\in \\Omega$$\n", | |
| "\n", | |
| "However, it can be shown that this does not conserve mass in the discrete formulation.\n", | |
| "\n", | |
| "\n", | |
| "Here we reproduce the results from Ceilia *et al.* (1990) demonstrating that the head-based formulation is not as good as the mixed-formulation.\n", | |
| "\n", | |
| "\n", | |
| "\n", | |
| "*Celia, Michael A., Efthimios T. Bouloutas, and Rebecca L. Zarba. \"<a href=\"http://www.webpages.uidaho.edu/ch/papers/Celia.pdf\">A general mass-conservative numerical solution for the unsaturated flow equation.</a>\" Water Resources Research 26.7 (1990): 1483-1496.*\n" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "collapsed": false, | |
| "input": [ | |
| "from SimPEG import *\n", | |
| "import Richards" | |
| ], | |
| "language": "python", | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "output_type": "stream", | |
| "stream": "stdout", | |
| "text": [ | |
| "Warning: mumps solver not available.\n" | |
| ] | |
| } | |
| ], | |
| "prompt_number": 1 | |
| }, | |
| { | |
| "cell_type": "code", | |
| "collapsed": false, | |
| "input": [ | |
| "M = mesh.TensorMesh([np.ones(40)])\n", | |
| "M.setCellGradBC('dirichlet')\n", | |
| "Ks = 9.4400e-03\n", | |
| "E = Richards.Haverkamp(Ks=np.log(Ks), A=1.1750e+06, gamma=4.74, \n", | |
| " alpha=1.6110e+06, theta_s=0.287, \n", | |
| " theta_r=0.075, beta=3.96)\n", | |
| "bc = np.array([-61.5,-20.7])\n", | |
| "h = np.zeros(M.nC) + bc[0]\n", | |
| "\n", | |
| "def getFields(timeStep,method):\n", | |
| " prob = Richards.RichardsProblem(M,E, timeStep=timeStep, timeEnd=360, \n", | |
| " boundaryConditions=bc, initialConditions=h, \n", | |
| " doNewton=False, method=method)\n", | |
| " return prob.field(np.log(Ks))\n", | |
| "\n", | |
| "Hs_M10 = getFields(10, 'mixed')\n", | |
| "Hs_M30 = getFields(30, 'mixed')\n", | |
| "Hs_M120= getFields(120,'mixed')\n", | |
| "Hs_H10 = getFields(10, 'head')\n", | |
| "Hs_H30 = getFields(30, 'head')\n", | |
| "Hs_H120= getFields(120,'head')" | |
| ], | |
| "language": "python", | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "output_type": "stream", | |
| "stream": "stdout", | |
| "text": [ | |
| "NewtonRoot stopped by maxIters. norm: 5.1942e-05\n", | |
| "NewtonRoot stopped by maxIters. norm: 1.0531e-06" | |
| ] | |
| }, | |
| { | |
| "output_type": "stream", | |
| "stream": "stdout", | |
| "text": [ | |
| "\n", | |
| "NewtonRoot stopped by maxIters. norm: 1.1545e-06" | |
| ] | |
| }, | |
| { | |
| "output_type": "stream", | |
| "stream": "stdout", | |
| "text": [ | |
| "\n", | |
| "NewtonRoot stopped by maxIters. norm: 2.2226e-06" | |
| ] | |
| }, | |
| { | |
| "output_type": "stream", | |
| "stream": "stdout", | |
| "text": [ | |
| "\n", | |
| "NewtonRoot stopped by maxIters. norm: 2.6211e-06" | |
| ] | |
| }, | |
| { | |
| "output_type": "stream", | |
| "stream": "stdout", | |
| "text": [ | |
| "\n" | |
| ] | |
| } | |
| ], | |
| "prompt_number": 2 | |
| }, | |
| { | |
| "cell_type": "code", | |
| "collapsed": false, | |
| "input": [ | |
| "figure(figsize=(13,5))\n", | |
| "subplot(121)\n", | |
| "plot(40-M.gridCC, Hs_M10[-1],'b-')\n", | |
| "plot(40-M.gridCC, Hs_M30[-1],'r-')\n", | |
| "plot(40-M.gridCC, Hs_M120[-1],'k-')\n", | |
| "title('Mixed Method');xlabel('Depth, cm');ylabel('Pressure Head, cm')\n", | |
| "legend(('dt = 10 sec','dt = 30 sec','dt = 120 sec'))\n", | |
| "subplot(122)\n", | |
| "plot(40-M.gridCC, Hs_H10[-1],'b-')\n", | |
| "plot(40-M.gridCC, Hs_H30[-1],'r-')\n", | |
| "plot(40-M.gridCC, Hs_H120[-1],'k-')\n", | |
| "title('Head-Based Method');xlabel('Depth, cm');ylabel('Pressure Head, cm')\n", | |
| "legend(('dt = 10 sec','dt = 30 sec','dt = 120 sec'))" | |
| ], | |
| "language": "python", | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "metadata": {}, | |
| "output_type": "pyout", | |
| "prompt_number": 3, | |
| "text": [ | |
| "<matplotlib.legend.Legend at 0x10fb352d0>" | |
| ] | |
| }, | |
| { | |
| "metadata": {}, | |
| "output_type": "display_data", | |
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+jE41/uLIEd3FLkRm27BhA8+ePaNy5cpcu3aNHj16aMsKFCjA6NGjadSoEYUK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| |
| "text": [ | |
| "<matplotlib.figure.Figure at 0x10fae6990>" | |
| ] | |
| } | |
| ], | |
| "prompt_number": 3 | |
| }, | |
| { | |
| "cell_type": "code", | |
| "collapsed": false, | |
| "input": [ | |
| "def function(var, ax, clim, tlt, i):\n", | |
| " ax.cla()\n", | |
| " linem, = ax.plot(40-M.gridCC, Hs_M10[i], 'r-', lw=1)\n", | |
| " lineh, = ax.plot(40-M.gridCC, Hs_H10[i], 'b-', lw=1)\n", | |
| " ax.legend(('mixed','head'))\n", | |
| " ax.set_title('Time %4.f seconds'%(i*10))\n", | |
| " \n", | |
| "M.video(Hs_H10,function,colorbar=False,figsize=(6,5))" | |
| ], | |
| "language": "python", | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "html": [ | |
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| " Your browser does not support the video tag.\n", | |
| "</video>" | |
| ], | |
| "metadata": {}, | |
| "output_type": "pyout", | |
| "prompt_number": 4, | |
| "text": [ | |
| "<matplotlib.animation.FuncAnimation at 0x10fb98f90>" | |
| ] | |
| } | |
| ], | |
| "prompt_number": 4 | |
| } | |
| ], | |
| "metadata": {} | |
| } | |
| ] | |
| } |
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