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‎documentation/md_examples.html

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<h1><a class="anchor" id="autotoc_md34"></a>
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2D Riemann Test (2D)</h1>
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<p>Reference: </p><blockquote class="doxtable">
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<p>&zwj;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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<p>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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</blockquote>
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<h2><a class="anchor" id="autotoc_md35"></a>
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Density Initial and Final Conditions</h2>
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<p><img src="alpha_rho1_initial-2D_riemann_test-example.png" alt="" width="45%" class="inline"/> <img src="alpha_rho1_final-2D_riemann_test-example.png" alt="" width="45%" class="inline"/></p>
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<h1><a class="anchor" id="autotoc_md36"></a>
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Shock Droplet (2D)</h1>
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<p>Reference: </p><blockquote class="doxtable">
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<p>&zwj;Panchal et. al., A Seven-Equation Diffused Interface Method for Resolved Multiphase Flows, JCP, 475 (2023) </p>
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<p>Panchal et. al., A Seven-Equation Diffused Interface Method for Resolved Multiphase Flows, JCP, 475 (2023) </p>
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</blockquote>
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<h2><a class="anchor" id="autotoc_md37"></a>
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Initial Condition</h2>
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Perfectly Stirred Reactor</h1>
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<p>Reference: </p><blockquote class="doxtable">
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<p>&zwj;G. B. Skinner and G. H. Ringrose, “Ignition Delays of a Hydrogen—Oxygen—Argon Mixture at Relatively Low Temperatures”, J. Chem. Phys., vol. 42, no. 6, pp. 2190–2192, Mar. 1965. Accessed: Oct. 13, 2024. [Online]. Available: <a href="https://doi.org/10.1063/1.1696266">https://doi.org/10.1063/1.1696266</a>. </p>
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<p>G. B. Skinner and G. H. Ringrose, “Ignition Delays of a Hydrogen—Oxygen—Argon Mixture at Relatively Low Temperatures”, J. Chem. Phys., vol. 42, no. 6, pp. 2190–2192, Mar. 1965. Accessed: Oct. 13, 2024. [Online]. Available: <a href="https://doi.org/10.1063/1.1696266">https://doi.org/10.1063/1.1696266</a>. </p>
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</blockquote>
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<div class="fragment"><div class="line">$ python3 analyze.py</div>
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<div class="line">Induction Times ([OH] &gt;= 1e-6):</div>
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Titarev-Toro problem (1D)</h1>
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<p>Reference: </p><blockquote class="doxtable">
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<p>&zwj;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>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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</blockquote>
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<h2><a class="anchor" id="autotoc_md41"></a>
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Initial Condition</h2>
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Shu-Osher problem (1D)</h1>
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<p>Reference: </p><blockquote class="doxtable">
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<p>&zwj;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>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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</blockquote>
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Initial Condition</h2>
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2D Triple Point (2D)</h1>
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<p>Reference: </p><blockquote class="doxtable">
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<p>&zwj;Trojak, W., &amp; Dzanic, T. Positivity-preserving discoutinous spectral element method for compressible multi-species flows. arXiv:2308.02426 </p>
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<p>Trojak, W., &amp; Dzanic, T. Positivity-preserving discoutinous spectral element method for compressible multi-species flows. arXiv:2308.02426 </p>
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</blockquote>
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Numerical Schlieren at Final Time</h2>
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<p><img src="final-2D_triple_point-example.png" alt="" height="400" class="inline"/></p>
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Lax shock tube problem (1D)</h1>
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<p>Reference: </p><blockquote class="doxtable">
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<p>&zwj;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>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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</blockquote>
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Initial Condition</h2>
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Lid-Driven Cavity Problem (2D)</h1>
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<p>Reference: </p><blockquote class="doxtable">
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<p>&zwj;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>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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</blockquote>
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<blockquote class="doxtable">
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<p>&zwj;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>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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</blockquote>
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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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1D Multi-Component Inert Shock Tube</h1>
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<p>Reference: </p><blockquote class="doxtable">
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<p>&zwj;P. J. Martínez Ferrer, R. Buttay, G. Lehnasch, and A. Mura, “A detailed verification procedure for compressible reactive multicomponent Navier–Stokes solvers”, Comput. &amp; Fluids, vol. 89, pp. 88–110, Jan. 2014. Accessed: Oct. 13, 2024. [Online]. Available: <a href="https://doi.org/10.1016/j.compfluid.2013.10.014">https://doi.org/10.1016/j.compfluid.2013.10.014</a> </p>
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<p>P. J. Martínez Ferrer, R. Buttay, G. Lehnasch, and A. Mura, “A detailed verification procedure for compressible reactive multicomponent Navier–Stokes solvers”, Comput. &amp; Fluids, vol. 89, pp. 88–110, Jan. 2014. Accessed: Oct. 13, 2024. [Online]. Available: <a href="https://doi.org/10.1016/j.compfluid.2013.10.014">https://doi.org/10.1016/j.compfluid.2013.10.014</a> </p>
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</blockquote>
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Initial Condition</h2>
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Isentropic vortex problem (2D)</h1>
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<p>Reference: </p><blockquote class="doxtable">
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<p>&zwj;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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<p>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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</blockquote>
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Density</h2>
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Taylor-Green Vortex (3D)</h1>
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<p>Reference: </p><blockquote class="doxtable">
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<p>&zwj;Hillewaert, K. (2013). TestCase C3.5 - DNS of the transition of the Taylor-Green vortex, Re=1600 - Introduction and result summary. 2nd International Workshop on high-order methods for CFD. </p>
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<p>Hillewaert, K. (2013). TestCase C3.5 - DNS of the transition of the Taylor-Green vortex, Re=1600 - Introduction and result summary. 2nd International Workshop on high-order methods for CFD. </p>
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Final Condition</h2>
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1D Multi-Component Reactive Shock Tube</h1>
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<p>References: </p><blockquote class="doxtable">
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<p>&zwj;P. J. Martínez Ferrer, R. Buttay, G. Lehnasch, and A. Mura, “A detailed verification procedure for compressible reactive multicomponent Navier–Stokes solvers”, Comput. &amp; Fluids, vol. 89, pp. 88–110, Jan. 2014. Accessed: Oct. 13, 2024. [Online]. Available: <a href="https://doi.org/10.1016/j.compfluid.2013.10.014">https://doi.org/10.1016/j.compfluid.2013.10.014</a> </p>
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<p>P. J. Martínez Ferrer, R. Buttay, G. Lehnasch, and A. Mura, “A detailed verification procedure for compressible reactive multicomponent Navier–Stokes solvers”, Comput. &amp; Fluids, vol. 89, pp. 88–110, Jan. 2014. Accessed: Oct. 13, 2024. [Online]. Available: <a href="https://doi.org/10.1016/j.compfluid.2013.10.014">https://doi.org/10.1016/j.compfluid.2013.10.014</a> </p>
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<p>&zwj;H. Chen, C. Si, Y. Wu, H. Hu, and Y. Zhu, “Numerical investigation of the effect of equivalence ratio on the propagation characteristics and performance of rotating detonation engine”, Int. J. Hydrogen Energy, Mar. 2023. Accessed: Oct. 13, 2024. [Online]. Available: <a href="https://doi.org/10.1016/j.ijhydene.2023.03.190">https://doi.org/10.1016/j.ijhydene.2023.03.190</a> </p>
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<p>H. Chen, C. Si, Y. Wu, H. Hu, and Y. Zhu, “Numerical investigation of the effect of equivalence ratio on the propagation characteristics and performance of rotating detonation engine”, Int. J. Hydrogen Energy, Mar. 2023. Accessed: Oct. 13, 2024. [Online]. Available: <a href="https://doi.org/10.1016/j.ijhydene.2023.03.190">https://doi.org/10.1016/j.ijhydene.2023.03.190</a> </p>
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Initial Condition</h2>

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