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. 
@article{MM_2020_32_6_a1,
     author = {M. D. Bragin and B. V. Rogov},
     title = {High-order bicompact schemes for numerical modelling of multispecies multi-reaction gas flows},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {21--36},
     publisher = {mathdoc},
     volume = {32},
     number = {6},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2020_32_6_a1/}
}
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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/