Geodesic
High-order bicompact schemes for numerical modelling of multispecies multi-reaction gas flows
Matematičeskoe modelirovanie, Tome 32 (2020) no. 6, pp. 21-36.

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Euler equations for multidimensional inviscid gas flows with multispecies and multi-reaction are considered. Using the Marchuk–Strang splitting method, an implicit numerical scheme for this system is constructed. Its convection part is computed by the bicompact scheme SDIRK3B4 of fourth order in space and third order in time, while its chemical part is computed by the $L$-stable Runge-Kutta method of second order. The SDIRK3B4 scheme is compared to the WENO5/SR scheme in case of one- and two-dimensional flows with detonation waves. It is shown, that the SDIRK3B4 scheme has the same factual accuracy as the WENO5/SR, but the former needs 20–40 times less time steps and does not require any special algorithms to suppress non-physical breakdown of detonation waves on relatively coarse meshes.
Keywords: gas dynamics, chemical reactions, detonation, bicompact schemes, implicit schemes, high-order schemes. 
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M. D. Bragin; B. V. Rogov. High-order bicompact schemes for numerical modelling of multispecies multi-reaction gas flows. Matematičeskoe modelirovanie, Tome 32 (2020) no. 6, pp. 21-36. http://geodesic.mathdoc.fr/item/MM_2020_32_6_a1/

[1] G. I. Marchuk, Metody rashchepleniia, Nauka, M., 1988, 263 pp.

[2] A. A. Samarskii, The theory of difference schemes, Marcel Dekker, New York, 2001, 786 pp. | MR | MR | Zbl

[3] N. N. Yanenko, The method of fractional steps: the solution of problems of mathematical physics in several variables, Springer-Verlag, Berlin, 1971, 160 pp. | MR | Zbl

[4] G. Strang, “On the construction and comparison of difference schemes”, SIAM J. Numer. Anal., 5:2 (1968), 506–517 | DOI | MR | Zbl

[5] V. A. Levin, I. S. Manuylovich, V. V. Markov, “Numerical simulation of spinning detonation in circular section channels”, Comp. Math. Math. Phys., 56:6 (2016), 1102–1117 | DOI | DOI | MR | Zbl

[6] B. Yu, L. Li, B. Zhang, J. Wang, “An approach to obtain the correct shock speed for Euler equations with stiff detonation”, Commun. Comput. Phys., 22:1 (2017), 259–284 | DOI | MR

[7] W. Wang, C. W. Shu, H. C. Yee, D. V. Kotov, B. Sjögreen, “High order finite difference methods with subcell resolution for stiff multispecies discontinuity capturing”, Commun. Comput. Phys., 17:2 (2015), 317–336 | DOI | MR | Zbl

[8] A. V. Danilin, A. V. Solovjev, A. M. Zaitsev, “Modifikatsiia skhemy «KABARE» dlia chislennogo modelirovaniia odnomernykh detonatsionnykh techenii s ispolzovaniem odnostadiinoi neobratimoi modeli khimicheskoi kinetiki”, Vychisl. Metody i Progr., 18:1 (2017), 1–10

[9] A. Lopato, P. Utkin, “Numerical study of detonation wave propagation in the variable cross section channel using unstructured computational grids”, J. Combustion, 2018 (2018), 3635797, 8 pp. | DOI

[10] P. Colella, A. Majda, V. Roytburd, “Theoretical and numerical structure for reacting shock waves”, SIAM J. Sci. Stat. Comp., 7:4 (1986), 1059–1080 | DOI | MR | Zbl

[11] W. Wang, C. W. Shu, H. C. Yee, B. Sjögreen, “High order finite difference methods with subcell resolution for advection equations with stiff source terms”, J. Comp. Phys., 231 (2012), 190–214 | DOI | MR | Zbl

[12] W. Bao, S. Jin, “The random projection method for hyperbolic conservation laws with stiff reaction terms”, J. Comp. Phys., 163:1 (2000), 216–248 | DOI | MR | Zbl

[13] W. Bao, S. Jin, “The random projection method for stiff multispecies detonation capturing”, J. Comp. Phys., 178:1 (2002), 37–57 | DOI | MR | Zbl

[14] L. Tosatto, L. Vigevano, “Numerical solution of under-resolved detonations”, J. Comp. Phys., 227 (2008), 2317–2343 | DOI | MR | Zbl

[15] M. D. Bragin, B. V. Rogov, “High-order bicompact schemes for shock-capturing computations of detonation waves”, Comp. Math. Math. Phys., 59:8 (2019), 1314–1323 | DOI | DOI | MR | Zbl

[16] M. D. Bragin, B. V. Rogov, “Minimal dissipation hybrid bicompact schemes for hyperbolic equations”, Comp. Math. Math. Phys., 56:6 (2016), 947–961 | DOI | DOI | MR | Zbl

[17] B. V. Rogov, “Dispersive and dissipative properties of the fully discrete bicompact schemes of the fourth order of spatial approximation for hyperbolic equations”, Appl. Numer. Math., 139 (2019), 136–155 | DOI | MR | Zbl

[18] R. Alexander, “Diagonally implicit Runge-Kutta methods for stiff O.D.E.'s”, SIAM J. Numer. Anal., 14:6 (1977), 1006–1021 | DOI | MR | Zbl

[19] M. D. Bragin, B. V. Rogov, “On exact dimensional splitting for a multidimensional scalar quasilinear hyperbolic conservation law”, Dokl. Math., 94:1 (2016), 382–386 | DOI | MR | Zbl

[20] M. D. Bragin, B. V. Rogov, “A conservative limiting method for bicompact schemes”, Keldysh Institute preprints, 2019, 008, 26 pp.

[21] M. D. Bragin, B. V. Rogov, “Bicompact schemes for multidimensional hyperbolic equations on Cartesian meshes with solution-based AMR”, Keldysh Institute Preprints, 2019, 011, 27 pp.