High‑Order Bicompact Schemes for Numerical Modeling of Multispecies Multi-Reaction Gas Flows

Abstract

Euler equations for multidimensional inviscid gas flows with multispecies and multi‑reaction are considered. By using the Marchuk–Strang splitting method, an implicit numerical scheme for this system is constructed. Its convection part is computed using the bicompact scheme SDIRK3B4 of fourth order in space and third order in time, while its chemical part is computed using the L-stable Runge–Kutta method of second order. The SDIRK3B4 scheme is compared with the WENO5/SR scheme in the case of one- and two-dimensional flows with detonation waves. It is shown that the SDIRK3B4 scheme has the same actual accuracy as the WENO5/SR, but the former needs fewer time steps by a factor of 20–40 and does not require any special algorithms to suppress the nonphysical breakdown of detonation waves on relatively coarse meshes.