Integrator::HeatConduction
==========================

:bdg-link-secondary-line:`src/Integrator/HeatConduction.H <../../doxygen/HeatConduction_8H_source.html>`

This implements a basic heat conduction method in Alamo.
The partial differential equation to be solved is

.. math::

   \frac{\partial T}{\partial t} = \alpha\,\Delta T

where :math:`T` is temperature, :math:`t` is time, and :math:`alpha` 
is the thermal diffusivity.
Integration is performed explicitly in time using forward Euler, and
differentiation is performed using the finite difference method.

.. container:: input-reference-math-loader

   :math:`\phantom{0}`

.. raw:: html

   <div class="input-reference-list">
     <article class="input-reference-item" id="input-heat-alpha-c74218353d">
       <header class="input-reference-item-header">
         <a class="input-reference-name" href="../../doxygen/HeatConduction_8H_source.html#l00078"><code>heat.alpha</code></a>
         <div class="input-reference-badges"><span class="input-reference-badge input-reference-badge-required">required</span> <span class="input-reference-badge input-reference-badge-meta">conditional</span></div>
       </header>
       <p class="input-reference-description">Diffusion coefficient <span class="math notranslate nohighlight">\(\alpha\)</span>. *This is an example of a required input variable - - program will terminate unless it is provided.*</p>
       <details class="input-reference-resolved">
         <summary>Names by executable <span>4 executables, 4 uses</span></summary>
         <div class="input-reference-resolved-body">
           <div class="input-reference-executable">
             <strong>alamo-2d-coverage-g++</strong>
             <div class="input-reference-paths">
               <code>heat.alpha</code>
             </div>
           </div>
           <div class="input-reference-executable">
             <strong>alamo-3d-coverage-g++</strong>
             <div class="input-reference-paths">
               <code>heat.alpha</code>
             </div>
           </div>
           <div class="input-reference-executable">
             <strong>thermoelastic-2d-coverage-g++</strong>
             <div class="input-reference-paths">
               <code>hc.heat.alpha</code>
             </div>
           </div>
           <div class="input-reference-executable">
             <strong>thermoelastic-3d-coverage-g++</strong>
             <div class="input-reference-paths">
               <code>hc.heat.alpha</code>
             </div>
           </div>
         </div>
       </details>
     </article>
     <article class="input-reference-item" id="input-heat-refinement-threshold-c95908e3db">
       <header class="input-reference-item-header">
         <a class="input-reference-name" href="../../doxygen/HeatConduction_8H_source.html#l00085"><code>heat.refinement_threshold</code></a>
         <div class="input-reference-badges"><span class="input-reference-badge input-reference-badge-default">0.01_K</span></div>
       </header>
       <p class="input-reference-description">Criterion for mesh refinement. *This is an example of a default input variable. The default value is provided here, not in the definition of the variable.*</p>
       <details class="input-reference-resolved">
         <summary>Names by executable <span>2 executables, 2 uses</span></summary>
         <div class="input-reference-resolved-body">
           <div class="input-reference-executable">
             <strong>thermoelastic-2d-coverage-g++</strong>
             <div class="input-reference-paths">
               <code>hc.heat.refinement_threshold</code>
             </div>
           </div>
           <div class="input-reference-executable">
             <strong>thermoelastic-3d-coverage-g++</strong>
             <div class="input-reference-paths">
               <code>hc.heat.refinement_threshold</code>
             </div>
           </div>
         </div>
       </details>
     </article>
     <article class="input-reference-item" id="input-ic-2124dd05bf">
       <header class="input-reference-item-header">
         <a class="input-reference-name" href="../../doxygen/HeatConduction_8H_source.html#l00089"><code>ic</code></a>
         <div class="input-reference-badges"><span class="input-reference-badge input-reference-badge-default">default</span> <span class="input-reference-badge input-reference-badge-option">constant</span> <span class="input-reference-badge input-reference-badge-option">expression</span> <span class="input-reference-badge input-reference-badge-option">sphere</span> <span class="input-reference-badge input-reference-badge-meta">conditional</span></div>
       </header>
       <p class="input-reference-description">Initial condition type.</p>
       <details class="input-reference-resolved">
         <summary>Names by executable <span>4 executables, 4 uses</span></summary>
         <div class="input-reference-resolved-body">
           <div class="input-reference-executable">
             <strong>alamo-2d-coverage-g++</strong>
             <div class="input-reference-paths">
               <code>ic.type</code>
             </div>
           </div>
           <div class="input-reference-executable">
             <strong>alamo-3d-coverage-g++</strong>
             <div class="input-reference-paths">
               <code>ic.type</code>
             </div>
           </div>
           <div class="input-reference-executable">
             <strong>thermoelastic-2d-coverage-g++</strong>
             <div class="input-reference-paths">
               <code>hc.ic.type</code>
             </div>
           </div>
           <div class="input-reference-executable">
             <strong>thermoelastic-3d-coverage-g++</strong>
             <div class="input-reference-paths">
               <code>hc.ic.type</code>
             </div>
           </div>
         </div>
       </details>
     </article>
     <article class="input-reference-item" id="input-bc-temp-9a62a07074">
       <header class="input-reference-item-header">
         <a class="input-reference-name" href="../../doxygen/HeatConduction_8H_source.html#l00093"><code>bc.temp</code></a>
         <div class="input-reference-badges"><span class="input-reference-badge input-reference-badge-default">default</span> <span class="input-reference-badge input-reference-badge-option">constant</span> <span class="input-reference-badge input-reference-badge-option">expression</span></div>
       </header>
       <p class="input-reference-description">Select BC object for temperature</p>
       <details class="input-reference-resolved">
         <summary>Names by executable <span>2 executables, 2 uses</span></summary>
         <div class="input-reference-resolved-body">
           <div class="input-reference-executable">
             <strong>thermoelastic-2d-coverage-g++</strong>
             <div class="input-reference-paths">
               <code>hc.bc.temp.type</code>
             </div>
           </div>
           <div class="input-reference-executable">
             <strong>thermoelastic-3d-coverage-g++</strong>
             <div class="input-reference-paths">
               <code>hc.bc.temp.type</code>
             </div>
           </div>
         </div>
       </details>
     </article>
     <article class="input-reference-item" id="input-method-f8c7a5b272">
       <header class="input-reference-item-header">
         <a class="input-reference-name" href="../../doxygen/HeatConduction_8H_source.html#l00097"><code>method</code></a>
         <div class="input-reference-badges"><span class="input-reference-badge input-reference-badge-option">realspace</span> <span class="input-reference-badge input-reference-badge-option">spectral</span></div>
       </header>
       <p class="input-reference-description">Select between using a realspace solve or the spectral method</p>
       <details class="input-reference-resolved">
         <summary>Names by executable <span>2 executables, 2 uses</span></summary>
         <div class="input-reference-resolved-body">
           <div class="input-reference-executable">
             <strong>thermoelastic-2d-coverage-g++</strong>
             <div class="input-reference-paths">
               <code>hc.method</code>
             </div>
           </div>
           <div class="input-reference-executable">
             <strong>thermoelastic-3d-coverage-g++</strong>
             <div class="input-reference-paths">
               <code>hc.method</code>
             </div>
           </div>
         </div>
       </details>
     </article>
   </div>