High-order bicompact schemes for shock-capturing computations of detonation waves

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.