AUSM‐like expression of HLLC and its all‐speed extension. (6th November 2019)

• Record Type: Journal Article
• Authors: Kitamura, Keiichi; Shima, Eiji
• Is Part Of: International journal for numerical methods in fluids. Volume 92:Number 4(2020)
• Page Start: 246
• Page End: 265
• Publication Date: 2019-11-06
• Subjects: all speeds -- AUSM -- finite volume method -- HLLC -- HLLCL -- SLAU; Fluid dynamics -- Mathematics -- Periodicals; 532
• DOI: 10.1002/fld.4782
• Languages: English
• ISSNs: 0271-2091

Abstract

Summary: Advection upstream splitting method (AUSM) and Harten‐Lax‐van Leer with contact (HLLC) are two popular families of flux functions. The AUSM is simple and requires no eigenstructure, which facilitates its extensions to general equations of state. Furthermore, one of its variants, simple low‐dissipation AUSM (SLAU), is applicable to all speeds and features removal of parameter setting by the user. HLLC, on the other hand, clearly defines three distinct waves in Riemann problem, namely, left‐running and right‐running acoustic waves, and entropy wave. This paper demonstrates that HLLC can be written in a very similar form with the AUSM family and that the similar manner in extending AUSM family to all speeds is easily incorporated into HLLC in this AUSM‐like form. Then, we combine the strengths of the both flux functions and offer a new inviscid numerical flux function within the framework of monotone upwind scheme for conservation laws (MUSCL) in computational fluid dynamics (CFD) for Euler and Navier‐Stokes equations. The resultant HLLC with low dissipation (HLLCL) numerical flux can compute low Mach number flows and sound propagations at the same time with high accuracy, as demonstrated by one‐dimensional and two‐dimensional numerical examples. Furthermore, the results indicate that its extensions to general fluids such as supercritical fluids are encouraging. Abstract : Harten‐Lax‐van Leer with contact (HLLC) is expressed in an advection upstream splitting method (AUSM)–like manner, and the AUSM‐like‐expressed HLLC is extended to all speeds as HLLC with low dissipation (HLLCL) flux. The HLLCL can compute both low speed flows and sound propagations.