Assessment of modern shock capturing schemes for all-speed flows in the OpenFOAM framework

Abstract

OpenFOAM is a widely used computational fluid dynamics (CFD) framework based on the finite volume method for solving a wide range of flow problems. However, its default numerical schemes, particularly the Kurganov-Noelle-Petrova (KNP) method used for shock capturing, are only low-order accurate. This work presents the implementation of modern high-order Riemann solvers along with AUSM+up (Advection Upstream Splitting Method) and LDFSS (Low Diffusion Flux Splitting Scheme) within the OpenFOAM environment. It evaluates them across test cases of increasing complexity. Results show that the default KNP scheme is robust but overly diffusive on coarse grids, suppressing flow features, while finer grids introduce spurious oscillations. The solver remains stable only under low Courant numbers but can tolerate mild numerical noise at higher values (around 0.5). A Total Variation Diminishing (TVD) Runge-Kutta time integration enhances stability while preserving accuracy. Among the tested flux schemes, HLLC (Harten-Lax-van Leer Contact) and its corrected variants HLLC-LM (Low-Mach correction) and HLLCP (pressure dissipation), as well as AUSM+up and LDFSS, all improve shock and contact-wave resolution on coarse grids. While the standard HLLC suffers from grid-aligned discontinuities, the corrected forms overcome these issues. AUSM+up introduces slightly higher dissipation and underperforms in deep subsonic regimes. In contrast, LDFSS provides comparable accuracy to HLLC-type solvers but is computationally expensive at very low Mach numbers and fails for strong unsteady shocks. The findings guide OpenFOAM users in selecting suitable shock-capturing schemes for specific flow regimes.