Low dissipative finite difference hybrid scheme by discontinuity sensor of detecting shock and material interface in multi-component compressible flows

Abstract

A discontinuity sensor for shock waves and material interfaces is proposed to construct a low dissipative scheme that consists of a weighted compact finite nonlinear scheme (WCNS) and central difference to address compressible multi-component flows. The Harten-Lax-van Leer and contact (HLLC) scheme is applied to capture shock waves through material interfaces. At the material interface, the overestimated quasi-conservative WCNS maintains the equilibriums of velocity, pressure, and temperature. The discontinuity sensor is composed of a Larrson shock sensor and a material interface sensor to distinguish between smooth and discontinuous regions, respectively. In the single-component shock-vortex interaction problem, the present scheme successfully captures shock waves with low numerical dissipation. In the multi-component shock-bubble interaction problem, Richtmyer-Meshkov instability problem, and triple-point problem, the simultaneous capturing of shock waves and material interfaces by the present scheme is demonstrated. The proposed scheme suppresses the numerical oscillation by shock waves and material interfaces; additionally, it successfully reduces the numerical dissipation in smooth regions.