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‎documentation/centerline_velocities-2D_lid_driven_cavity-example.png

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</div><!--header-->
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<div class="contents">
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<div class="textblock"><p><a class="anchor" id="md_readme"></a> </p>
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User Documentation</h1>
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<li><a class="el" href="md_authors.html">MFC's Authors</a></li>
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<li><a class="el" href="md_references.html">References</a></li>
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</ul>
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Code/API Documentation</h1>
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<p>MFC's three codes have their own documentation:</p>
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‎documentation/md_case.html

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<td class="markdownTableBodyRight"><code>bc_[x,y,z]\beg[end]</code> </td><td class="markdownTableBodyCenter">Integer </td><td class="markdownTableBodyLeft">Beginning [ending] boundary condition in the $[x,y,z]$-direction (negative integer, see table Boundary Conditions) </td></tr>
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<td class="markdownTableBodyRight"><code>bc_[x,y,z]\vb[1,2,3]</code>‡ </td><td class="markdownTableBodyCenter">Real </td><td class="markdownTableBodyLeft">Velocity in the (x,1), (y, 2), (z,3) direction applied to <code>bc_[x,y,z]beg</code> </td></tr>
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<td class="markdownTableBodyRight"><code>bc_[x,y,z]\ve[1,2,3]</code>‡ </td><td class="markdownTableBodyCenter">Real </td><td class="markdownTableBodyLeft">Velocity in the (x,1), (y, 2), (z,3) direction applied to <code>bc_[x,y,z]end</code> </td></tr>
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<td class="markdownTableBodyRight"><code>model_eqns</code> </td><td class="markdownTableBodyCenter">Integer </td><td class="markdownTableBodyLeft">Multicomponent model: [1] $\Gamma/\Pi_\infty$; [2] 5-equation; [3] 6-equation\%;%[4] 4-equation </td></tr>
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<td class="markdownTableBodyRight"><code>alt_soundspeed</code> * </td><td class="markdownTableBodyCenter">Logical </td><td class="markdownTableBodyLeft">Alternate sound speed and $K \nabla \cdot u$ for 5-equation model </td></tr>
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<li>* Options that work only with <code>model_eqns</code> $=2$.</li>
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<li>† Options that work only with <code>cyl_coord</code> $=$ <code>False</code>.</li>
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<li>‡ Options that work only with <code>bc_[x,y,z]%[beg,end] = -15</code> and/or <code>bc_[x,y,z]%[beg,end] = -16</code></li>
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<p>The table lists simulation algorithm parameters. The parameters are used to specify options in algorithms that are used to integrate the governing equations of the multi-component flow based on the initial condition. Models and assumptions that are used to formulate and discritize the governing equations are described in <a href="references.md#Bryngelson19">Bryngelson et al. (2019)</a>. Details of the simulation algorithms and implementation of the WENO scheme can be found in <a href="references.md#Coralic15">Coralic (2015)</a>.</p>
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<li><code>bc_[x,y,z]%[beg,end]</code> specifies the boundary conditions at the beginning and the end of domain boundaries in each coordinate direction by a negative integer from -1 through -12. See table Boundary Conditions for details.</li>
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<li><code>bc_[x,y,z]\vb[1,2,3]</code> specifies the velocity in the (x,1), (y,2), (z,3) direction applied to <code>bc_[x,y,z]beg</code> when using <code>bc_[x,y,z]beg = -16</code>. Tangential velocities require viscosity, <code>weno_avg = T</code>, and <code>bc_[x,y,z]beg = -16</code> to work properly. Normal velocities require <code>bc_[x,y,z]\end = -15</code> or <code>\bc_[x,y,z]\end = -16</code> to work properly.</li>
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<li><code>bc_[x,y,z]\ve[1,2,3]</code> specifies the velocity in the (x,1), (y,2), (z,3) direction applied to <code>bc_[x,y,z]beg</code> when using <code>bc_[x,y,z]end = -16</code>. Tangential velocities require viscosity, <code>weno_avg = T</code>, and <code>bc_[x,y,z]\end = 16</code> to work properly. Normal velocities require <code>bc_[x,y,z]\end = -15</code> or <code>\bc_[x,y,z]\end = -16</code> to work properly.</li>
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<li><code>model_eqns</code> specifies the choice of the multi-component model that is used to formulate the dynamics of the flow using integers from 1 through 3. <code>model_eqns</code> $=$ 1, 2, and 3 correspond to $\Gamma$-$\Pi_\infty$ model (<a href="references.md#Johnsen08">Johnsen, 2008</a>), 5-equation model (<a href="references.md#Allaire02">Allaire et al., 2002</a>), and 6-equation model (<a href="references.md#Saurel09">Saurel et al., 2009</a>), respectively. The difference of the two models is assessed by (<a href="references.md#Schmidmayer19">Schmidmayer et al., 2019</a>). Note that some code parameters are only compatible with 5-equation model.</li>
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<li><code>alt_soundspeed</code> activates the source term in the advection equations for the volume fractions, $K\nabla\cdot \underline{u}$, that regularizes the speed of sound in the mixture region when the 5-equation model is used. The effect and use of the source term are assessed by <a href="references.md#Schmidmayer19">Schmidmayer et al., 2019</a>.</li>
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<li><code>adv_alphan</code> activates the advection equations of all the components of fluid. If this parameter is set false, the void fraction of $N$-th component is computed as the residual of the void fraction of the other components at each cell:</li>

‎documentation/md_examples.html

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Isentropic vortex problem (2D)</h1>
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<p>Reference: Coralic, V., &amp; Colonius, T. (2014). Finite-volume Weno scheme for viscous compressible multicomponent flows. Journal of Computational Physics, 274, 95–121. <a href="https://doi.org/10.1016/j.jcp.2014.06.003">https://doi.org/10.1016/j.jcp.2014.06.003</a></p>
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Shu-Osher problem (1D)</h1>
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<p>Reference: C. W. Shu, S. Osher, Efficient implementation of essentially non-oscillatory shock-capturing schemes, Journal of Computational Physics 77 (2) (1988) 439–471. doi:10.1016/0021-9991(88)90177-5.</p>
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<p>Reference: V. A. Titarev, E. F. Toro, Finite-volume WENO schemes for three-dimensional conservation laws, Journal of Computational Physics 201 (1) (2004) 238–260.</p>
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<p>Reference: Panchal et. al., A Seven-Equation Diffused Interface Method for Resolved Multiphase Flows, JCP, 475 (2023)</p>
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<div class="fragment"><div class="line">./mfc.sh run examples/3D_weak_scaling/case.py 4 -t pre_process simulation \</div>
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<div class="line"> -e batch -p mypartition -N 8 -n 2 -w &quot;01:00:00&quot; -# &quot;MFC Weak Scaling&quot; \</div>
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<p>Reference: P. D. Lax, Weak solutions of nonlinear hyperbolic equations and their numerical computation, Communications on pure and applied mathematics 7 (1) (1954) 159–193.</p>
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<p>Reference: Coralic, V., &amp; Colonius, T. (2014). Finite-volume Weno scheme for viscous compressible multicomponent flows. Journal of Computational Physics, 274, 95–121. <a href="https://doi.org/10.1016/j.jcp.2014.06.003">https://doi.org/10.1016/j.jcp.2014.06.003</a></p>
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Lid-Driven Cavity Problem (2D)</h1>
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<p>Reference: Bezgin, D. A., &amp; Buhendwa A. B., &amp; Adams N. A. (2022). JAX-FLUIDS: A fully-differentiable high-order computational fluid dynamics solver for compressible two-phase flows. arXiv:2203.13760</p>
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<p>Reference: Ghia, U., &amp; Ghia, K. N., &amp; Shin, C. T. (1982). High-re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method. Journal of Computational Physics, 48, 387-411</p>
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<p>Video: <a href="https://youtube.com/shorts/JEP28scZrBM?feature=share">https://youtube.com/shorts/JEP28scZrBM?feature=share</a></p>
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<p>Reference: Chamarthi, A., &amp; Hoffmann, N., &amp; Nishikawa, H., &amp; Frankel S. (2023). Implicit gradients based conservative numerical scheme for compressible flows. arXiv:2110.05461</p>
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</div></div><!-- contents -->

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