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‎documentation/md_examples.html‎

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<div class="contents">
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<div class="textblock"><p><a class="anchor" id="autotoc_md24"></a> </p>
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<h1><a class="anchor" id="autotoc_md25"></a>
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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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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>
133+
<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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<h2><a class="anchor" id="autotoc_md26"></a>
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Density Initial Condition</h2>
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Final Condition</h2>
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<div class="image">
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<img src="alpha_rho1_initial-2D_riemann_test-example.png" alt=""/>
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<img src="final_condition-2D_lid_driven_cavity-example.png" alt=""/>
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<div class="caption">
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Density</div></div>
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Final Condition</div></div>
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<h2><a class="anchor" id="autotoc_md27"></a>
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Density Final Condition</h2>
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Centerline Velocities</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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<img src="centerline_velocities-2D_lid_driven_cavity-example.png" alt=""/>
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<div class="caption">
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Density Norms</div></div>
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Centerline Velocities</div></div>
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<h1><a class="anchor" id="autotoc_md28"></a>
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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>
148+
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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<h2><a class="anchor" id="autotoc_md29"></a>
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Initial Condition</h2>
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Density 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="alpha_rho1_initial-2D_riemann_test-example.png" alt=""/>
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<div class="caption">
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Initial Condition</div></div>
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Density</div></div>
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<h2><a class="anchor" id="autotoc_md30"></a>
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Result</h2>
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Density Final Condition</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="alpha_rho1_final-2D_riemann_test-example.png" alt=""/>
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<div class="caption">
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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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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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2D Hardcodied IC Example</h1>
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<h2><a class="anchor" id="autotoc_md32"></a>
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Density</h2>
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Initial Condition</h2>
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<div class="image">
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<img src="alpha_rho1-2D_isentropicvortex-example.png" alt=""/>
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<img src="initial-2D_hardcodied_ic-example.png" alt=""/>
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<div class="caption">
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Density</div></div>
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Initial Condition</div></div>
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<h2><a class="anchor" id="autotoc_md33"></a>
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Density Norms</h2>
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<div class="image">
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<img src="density_norms-2D_isentropicvortex-example.png" alt=""/>
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<div class="caption">
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Density Norms</div></div>
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<h1><a class="anchor" id="autotoc_md34"></a>
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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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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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<h1><a class="anchor" id="autotoc_md34"></a>
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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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<h2><a class="anchor" id="autotoc_md35"></a>
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Initial Condition</h2>
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<div class="image">
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<img src="initial-2D_shockdroplet-example.png" alt=""/>
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Initial Condition</div></div>
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<h2><a class="anchor" id="autotoc_md36"></a>
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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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<h1><a class="anchor" id="autotoc_md37"></a>
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<div class="image">
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<img src="result-1D_titarevtorro-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_md37"></a>
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3D Weak Scaling</h1>
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<p>The <a href="case.py"><b>3D_weak_scaling</b></a> case depends on two parameters:</p>
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<ul>
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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</div>
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</div><!-- fragment --><h1><a class="anchor" id="autotoc_md38"></a>
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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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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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<h2><a class="anchor" id="autotoc_md39"></a>
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Initial Condition</h2>
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<div class="image">
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<img src="initial-1D_laxshocktube-example.png" alt=""/>
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<img src="initial-2D_shockdroplet-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_md40"></a>
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Result</h2>
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<div class="image">
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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_md41"></a>
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2D Hardcodied IC Example</h1>
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<p><img src="result-2D_shockdroplet-example.png" alt="" class="inline" title="Result"/> </p>
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<h1><a class="anchor" id="autotoc_md41"></a>
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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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<h2><a class="anchor" id="autotoc_md42"></a>
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Initial Condition</h2>
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Density</h2>
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<div class="image">
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<img src="initial-2D_hardcodied_ic-example.png" alt=""/>
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<img src="alpha_rho1-2D_isentropicvortex-example.png" alt=""/>
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<div class="caption">
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Initial Condition</div></div>
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Density</div></div>
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<h2><a class="anchor" id="autotoc_md43"></a>
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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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<h1><a class="anchor" id="autotoc_md44"></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>
228-
<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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Density Norms</h2>
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<div class="image">
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<img src="density_norms-2D_isentropicvortex-example.png" alt=""/>
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<div class="caption">
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Density Norms</div></div>
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<h1><a class="anchor" id="autotoc_md44"></a>
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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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<h2><a class="anchor" id="autotoc_md45"></a>
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Final Condition</h2>
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Initial Condition</h2>
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<div class="image">
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<img src="final_condition-2D_lid_driven_cavity-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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Final Condition</div></div>
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Initial Condition</div></div>
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<h2><a class="anchor" id="autotoc_md46"></a>
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Centerline Velocities</h2>
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Result</h2>
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<div class="image">
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<img src="centerline_velocities-2D_lid_driven_cavity-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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Centerline Velocities</div></div>
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Result</div></div>
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<h1><a class="anchor" id="autotoc_md47"></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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‎documentation/search/all_17.js‎

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