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           42   <section id="the-sphere-documentation">
           43 <h1>The sphere documentation<a class="headerlink" href="#the-sphere-documentation" title="Link to this heading">¶</a></h1>
           44 <p><code class="docutils literal notranslate"><span class="pre">sphere</span></code> is a 3D DEM particle simulator with optional coupled fluid solvers.
           45 The same source tree can be built for CUDA GPUs or OpenMP CPUs.</p>
           46 <p>Start with <a class="reference internal" href="quickstart.html"><span class="doc">Quick start</span></a> for installation and build commands, then use the
           47 model and API chapters for setup, execution, and analysis details.</p>
           48 <p><code class="docutils literal notranslate"><span class="pre">sphere</span></code> is developed by Anders Damsgaard as part as his Ph.D. project, under
           49 supervision of David Lundbek Egholm and Jan A. Piotrowski, all of the Department
           50 of Geoscience, Aarhus University, Denmark. The author welcomes interested third
           51 party developers. This document is a work in progress.</p>
           52 <p>Contact: Anders Damsgaard, <a class="reference external" href="https://adamsgaard.dk">https://adamsgaard.dk</a>,
           53 <a class="reference external" href="mailto:anders&#46;damsgaard&#37;&#52;&#48;geo&#46;au&#46;dk">mailto:anders<span>&#46;</span>damsgaard<span>&#64;</span>geo<span>&#46;</span>au<span>&#46;</span>dk</a></p>
           54 <section id="contents">
           55 <h2>Contents<a class="headerlink" href="#contents" title="Link to this heading">¶</a></h2>
           56 <div class="toctree-wrapper compound">
           57 <ul>
           58 <li class="toctree-l1"><a class="reference internal" href="quickstart.html">Quick start</a><ul>
           59 <li class="toctree-l2"><a class="reference internal" href="quickstart.html#requirements">Requirements</a></li>
           60 <li class="toctree-l2"><a class="reference internal" href="quickstart.html#build">Build</a></li>
           61 <li class="toctree-l2"><a class="reference internal" href="quickstart.html#run-checks">Run checks</a></li>
           62 <li class="toctree-l2"><a class="reference internal" href="quickstart.html#python-workflow">Python workflow</a></li>
           63 <li class="toctree-l2"><a class="reference internal" href="quickstart.html#build-documentation">Build documentation</a></li>
           64 </ul>
           65 </li>
           66 <li class="toctree-l1"><a class="reference internal" href="introduction.html">Introduction</a><ul>
           67 <li class="toctree-l2"><a class="reference internal" href="introduction.html#workflow">Workflow</a></li>
           68 <li class="toctree-l2"><a class="reference internal" href="introduction.html#updating-sphere">Updating sphere</a></li>
           69 </ul>
           70 </li>
           71 <li class="toctree-l1"><a class="reference internal" href="dem.html">Discrete element method</a><ul>
           72 <li class="toctree-l2"><a class="reference internal" href="dem.html#contact-search">Contact search</a></li>
           73 <li class="toctree-l2"><a class="reference internal" href="dem.html#contact-interaction">Contact interaction</a></li>
           74 <li class="toctree-l2"><a class="reference internal" href="dem.html#temporal-integration">Temporal integration</a></li>
           75 </ul>
           76 </li>
           77 <li class="toctree-l1"><a class="reference internal" href="cfd.html">Fluid simulation and particle-fluid interaction</a><ul>
           78 <li class="toctree-l2"><a class="reference internal" href="cfd.html#derivation-of-the-navier-stokes-equations-with-porosity">Derivation of the Navier Stokes equations with porosity</a></li>
           79 <li class="toctree-l2"><a class="reference internal" href="cfd.html#porosity-estimation">Porosity estimation</a></li>
           80 <li class="toctree-l2"><a class="reference internal" href="cfd.html#particle-fluid-interaction">Particle-fluid interaction</a></li>
           81 <li class="toctree-l2"><a class="reference internal" href="cfd.html#fluid-dynamics-solution-procedure-by-operator-splitting">Fluid dynamics solution procedure by operator splitting</a></li>
           82 <li class="toctree-l2"><a class="reference internal" href="cfd.html#boundary-conditions">Boundary conditions</a></li>
           83 <li class="toctree-l2"><a class="reference internal" href="cfd.html#numerical-implementation">Numerical implementation</a></li>
           84 </ul>
           85 </li>
           86 <li class="toctree-l1"><a class="reference internal" href="python_api.html">Python API</a><ul>
           87 <li class="toctree-l2"><a class="reference internal" href="python_api.html#using-the-module">Using the module</a></li>
           88 <li class="toctree-l2"><a class="reference internal" href="python_api.html#sample-usage">Sample usage</a></li>
           89 <li class="toctree-l2"><a class="reference internal" href="python_api.html#module-sphere">The <code class="docutils literal notranslate"><span class="pre">sphere</span></code> module</a></li>
           90 </ul>
           91 </li>
           92 <li class="toctree-l1"><a class="reference internal" href="sphere_internals.html">Sphere internals</a><ul>
           93 <li class="toctree-l2"><a class="reference internal" href="sphere_internals.html#command-line-interface">Command-line interface</a></li>
           94 <li class="toctree-l2"><a class="reference internal" href="sphere_internals.html#execution-pipeline">Execution pipeline</a></li>
           95 <li class="toctree-l2"><a class="reference internal" href="sphere_internals.html#numerical-algorithm">Numerical algorithm</a></li>
           96 <li class="toctree-l2"><a class="reference internal" href="sphere_internals.html#memory-layout">Memory layout</a></li>
           97 <li class="toctree-l2"><a class="reference internal" href="sphere_internals.html#performance">Performance</a></li>
           98 <li class="toctree-l2"><a class="reference internal" href="sphere_internals.html#compilation">Compilation</a></li>
           99 <li class="toctree-l2"><a class="reference internal" href="sphere_internals.html#c-reference">C++ reference</a></li>
          100 </ul>
          101 </li>
          102 </ul>
          103 </div>
          104 </section>
          105 <section id="indices-and-tables">
          106 <h2>Indices and tables<a class="headerlink" href="#indices-and-tables" title="Link to this heading">¶</a></h2>
          107 <ul class="simple">
          108 <li><p><a class="reference internal" href="genindex.html"><span class="std std-ref">Index</span></a></p></li>
          109 <li><p><a class="reference internal" href="search.html"><span class="std std-ref">Search Page</span></a></p></li>
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          122     <h3><a href="#">Table of Contents</a></h3>
          123     <ul>
          124 <li><a class="reference internal" href="#">The sphere documentation</a><ul>
          125 <li><a class="reference internal" href="#contents">Contents</a></li>
          126 <li><a class="reference internal" href="#indices-and-tables">Indices and tables</a></li>
          127 </ul>
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