Accurate and Robust Roe-Type Scheme for Multicomponent Chemical Reaction Flows

Over the past few decades, the numerical shock instability of the Roe scheme has remained a subject of intensive study in computational fluid dynamics, with extensive research efforts dedicated to investigating its mechanisms and developing effective strategies to mitigate the instability. However, most of these studies have been conducted within the framework of Euler flows. We note that, in simulations of multicomponent chemical reaction flows, the use of the Roe scheme for convective flux computation can also give rise to analogous shock anomalies. To enhance its robustness in simulating multicomponent chemical reaction flows, we construct two functions based on the pressure ratio and the temperature ratio to detect the shock wave and the combustion wave, respectively, and then introduce the entropy wave viscosity and the shear wave viscosity into the computation of numerical fluxes in the vicinity of shock waves and combustion waves. Since the added numerical viscosity is confined only to the vicinity of shock waves and combustion waves, the proposed scheme preserves the low-dissipation property of the Roe scheme for flowfield structures such as contact waves, rarefaction waves, and shear layers. Numerical results of various complex flows demonstrate that the proposed scheme, compared with the classical Roe scheme, exhibits significantly enhanced stability for strong shock waves and accurately captures combustion waves.