A carbuncle cure for the Harten-Lax-van Leer contact (HLLC) scheme using a novel velocity-based sensor

doi:10.1007/s10483-021-2762-6

Abstract

Abstract: A hybrid numerical flux scheme is proposed by adapting the carbuncle-free modified Harten-Lax-van Leer contact (HLLCM) scheme to smoothly revert to the Harten-Lax-van Leer contact (HLLC) scheme in regions of shear. This hybrid scheme, referred to as the HLLCT scheme, employs a novel, velocity-based shear sensor. In contrast to the non-local pressure-based shock sensors often used in carbuncle cures, the proposed shear sensor can be computed in a localized manner meaning that the HLLCT scheme can be easily introduced into existing codes without having to implement additional data structures. Through numerical experiments, it is shown that the HLLCT scheme is able to resolve shear layers accurately without succumbing to the shock instability.

Key words: carbuncle, shock instability, Euler equation, numerical flux, Harten-Lax-van Leer contact (HLLC) scheme

2010 MSC Number:

U. S. VEVEK, B. ZANG, T. H. NEW. A carbuncle cure for the Harten-Lax-van Leer contact (HLLC) scheme using a novel velocity-based sensor. Applied Mathematics and Mechanics (English Edition), 2021, 42(9): 1259-1278.

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