A numerically stable and low dissipation shock-capturing scheme

It is well known that the Harten-Lax-van Leer with contact (HLLC) scheme suffers from unstable performance in capturing strong multi-dimensional shock waves, which impedes its application in high-Mach-number flows. This paper presents a simple strategy to develop a stable HLLC-type scheme for three-dimensional inviscid Euler equations. The conventional HLLC flux is split into a dissipative HLL flux and an anti-diffusion term. The improvement of the numerical stability, justified by stability analyses and numerical experiments, is achieved by using a sufficiently smooth control function to adjust the numerical dissipation term of the transverse flux adjacent to the shock wave. In addition, the simple THINC (tangent of hyperbola for interface capturing) reconstruction method and the BVD (boundary variation diminishing) algorithm are employed to reduce the density difference in the numerical dissipation term, thus further improving the resolution for contact discontinuities. The numerical results of one- to three-dimensional benchmark examples demonstrate the proposed scheme’s high resolution for contact discontinuities and stability for multi-dimensional strong shock waves. The numerical results of a shock/boundary-layer interaction problem promise the future application of the proposed local anti-diffusion control method in simulating viscous flows. The modularization of the proposed scheme and its integration into Computational Fluid Dynamics software to simulate, for instance, hypersonic flows,multi-component chemical reaction flows, and turbulent combustion are worthy of further research in the future.