A diffusion-regulated scheme for the compressible Navier–Stokes equations using a boundary-layer sensor

Abstract

A new formulation to regulate the numerical diffusion of the Local Lax–Friedrichs (LLF) scheme for the accurate computation of high-speed viscous flows is proposed. This is achieved by modifying the diffusion regulation (DR) parameter of the DRLLF scheme originally proposed by Jaisankar and Raghurama Rao for the Euler equations. The modified version of the DR parameter operates based on a boundary layer sensor in such a way that the numerical diffusion is further reduced inside the viscous zone only and in the outer inviscid zone the parameter reverts back to the original inviscid formulation. This new scheme is named as the DRLLF-Viscous (DRLLFV) scheme. Test cases of viscous supersonic flow over a flat plate and hypersonic flow over a ramped surface are computed using the new scheme and compared with the AUSM scheme, DRLLF scheme and van Leer's Flux Vector Splitting (FVS) scheme. Comparisons with the literature show that the DRLLFV scheme resolves the boundary layer including flow separation more accurately than van Leer's FVS and DRLLF schemes and nearly as accurately as the AUSM scheme. In the inviscid zone, the DRLLFV scheme captures the leading-edge shock better than the rest of the schemes. If the overall results in both the viscous and inviscid regions are considered, the new scheme is seen to perform better than the AUSM scheme.