Abstract:
An implicit scheme with splitting with respect to physical processes is proposed for a stiff system of two-dimensional Euler gas dynamics equations with chemical source terms. For the first time, convection is computed using a bicompact scheme that is fourth-order accurate in space and third-order accurate in time. This high-order bicompact scheme is $L$-stable in time. It employs a conservative limiting method and Cartesian meshes with solution-based adaptive mesh refinement. The chemical reactions are computed using an $L$-stable second-order Runge–Kutta scheme. The developed scheme is successfully tested as applied to several problems concerning detonation wave propagation in a two-species ideal gas with a single combustion reaction. The advantages of bicompact schemes over the popular MUSCL and WENO5 schemes as applied to shock-capturing computations of detonation waves are discussed.
Key words:gas dynamics, chemical reactions, stiff systems, bicompact schemes, high-order accurate schemes, implicit schemes, adaptive Cartesian meshes.
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