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‎documentation/doxygen.css‎

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‎documentation/md_examples.html‎

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<div class="textblock"><p><a class="anchor" id="autotoc_md27"></a></p>
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<h1><a class="anchor" id="autotoc_md28"></a>
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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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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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Initial Condition</h2>
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Density</h2>
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<img src="alpha_rho1-2D_isentropicvortex-example.png" alt=""/>
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Initial Condition</div></div>
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Density</div></div>
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Result</h2>
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Density Norms</h2>
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<img src="result-1D_shuosher_old-example.png" alt=""/>
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Result</div></div>
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Density Norms</div></div>
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<h1><a class="anchor" id="autotoc_md31"></a>
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Rayleigh-Taylor Instability (3D)</h1>
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<h2><a class="anchor" id="autotoc_md32"></a>
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Final Condition</h2>
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<div class="image">
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Final Condition</div></div>
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<h2><a class="anchor" id="autotoc_md33"></a>
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Centerline Velocities</h2>
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<p><img src="linear_theory.jpg" alt="Linear Theory Comparison" class="inline"/></p>
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<h1><a class="anchor" id="autotoc_md34"></a>
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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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Centerline Velocities</h2>
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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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Initial Condition</h2>
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Initial Condition</div></div>
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Result</h2>
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Result</div></div>
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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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Shock Droplet (2D)</h1>
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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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Density</h2>
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Initial Condition</h2>
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Initial Condition</div></div>
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Lax shock tube problem (1D)</h1>
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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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Result</h2>
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<p><img src="result-2D_shockdroplet-example.png" alt="" class="inline" title="Result"/> </p>
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Titarev-Toro problem (1D)</h1>
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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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Initial Condition</h2>
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2D Hardcodied IC Example</h1>
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Final Condition</h2>
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Final Condition</div></div>
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Centerline Velocities</h2>
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Shock Droplet (2D)</h1>
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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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Initial Condition</h2>
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Result</h2>
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Strong- &amp; Weak-scaling</h1>
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<p>The <a href="case.py"><b>Scaling</b></a> case can exercise both weak- and strong-scaling. It adjusts itself depending on the number of requested ranks.</p>
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<p>This directory also contains a collection of scripts used to test strong-scaling on OLCF Frontier. They required modifying MFC to collect some metrics but are meant to serve as a reference to users wishing to run similar experiments.</p>
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<p>Pass <code>--scaling weak</code>. The <code>--memory</code> option controls (approximately) how much memory each rank should use, in Gigabytes. The number of cells in each dimension is then adjusted according to the number of requested ranks and an approximation for the relation between cell count and memory usage. The problem size increases linearly with the number of ranks.</p>
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<p>Pass <code>--scaling strong</code>. The <code>--memory</code> option controls (approximately) how much memory should be used in total during simulation, across all ranks, in Gigabytes. The problem size remains constant as the number of ranks increases.</p>
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<p>For example, to run a weak-scaling test that uses ~4GB of GPU memory per rank on 8 2-rank nodes with case optimization, one could:</p>
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<div class="fragment"><div class="line">./mfc.sh run examples/scaling/case.py -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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<div class="line"> --case-optimization -j 32 -- --scaling weak --memory 4</div>
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2D Riemann Test (2D)</h1>
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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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2D Hardcodied IC Example</h1>
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Initial Condition</h2>
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Density Final Condition</h2>
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Result</h2>
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<p><img src="result-2D_hardcodied_ic-example.png" alt="" class="inline" title="Result"/> </p>
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Rayleigh-Taylor Instability (2D)</h1>
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Final Condition</h2>
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Titarev-Toro problem (1D)</h1>
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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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Final Condition</div></div>
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Centerline Velocities</h2>
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Lax shock tube problem (1D)</h1>
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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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Initial Condition</h2>
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<div class="image">
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<img src="initial-1D_titarevtorro-example.png" alt=""/>
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<img src="initial-1D_laxshocktube-example.png" alt=""/>
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<div class="caption">
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Initial Condition</div></div>
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<h2><a class="anchor" id="autotoc_md58"></a>
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Result</h2>
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<div class="image">
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<img src="result-1D_titarevtorro-example.png" alt=""/>
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<img src="result-1D_laxshocktube-example.png" alt=""/>
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<div class="caption">
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Result</div></div>
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<h1><a class="anchor" id="autotoc_md59"></a>
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Rayleigh-Taylor Instability (2D)</h1>
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2D Riemann Test (2D)</h1>
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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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Final Condition</h2>
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Density Initial Condition</h2>
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<img src="final_condition-2D_rayleigh_taylor-example.png" alt=""/>
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<img src="alpha_rho1_initial-2D_riemann_test-example.png" alt=""/>
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<div class="caption">
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Final Condition</div></div>
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Density</div></div>
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Centerline Velocities</h2>
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<p><img src="linear_theory.jpg" alt="Linear Theory Comparison" class="inline"/> </p>
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Density Final Condition</h2>
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<div class="image">
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<img src="alpha_rho1_final-2D_riemann_test-example.png" alt=""/>
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<div class="caption">
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Density Norms</div></div>
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