A unified construction of all-speed HLL-type schemes for hypersonic heating computations

TL;DR

This paper introduces a unified framework for all-speed HLL-type schemes that improve shock robustness and low-Mach number accuracy, enabling reliable hypersonic heating simulations across diverse flow regimes.

Contribution

A novel unified construction method for all-speed HLL-type schemes that integrates shock robustness and low-Mach fixes, demonstrated through ASHLLC and ASHLLEM solvers.

Findings

Schemes maintain original properties while enhancing accuracy and robustness.

Effective across low-Mach to hypersonic flow regimes.

Numerical results confirm reliability for hypersonic heating computations.

Abstract

In this paper, a unified framework to develop all-speed HLL-type schemes for hypersonic heating computations is constructed. Such a unified construction method combines two effective improving techniques: a shock robustness improvement and a low-Mach number fix. It is implemented by properly modifying the approximate solutions of the local Riemann problem in the HLL framework, resulting in two all-speed HLL-type schemes, namely ASHLLC and ASHLLEM solvers. Results from both numerical analysis and experiments demonstrate that the newly proposed schemes not only preserve desirable properties of their original versions, but are also able to provide accurate and robust solutions for complex flows ranging from low-Mach number incompressible to hypersonic compressible regimes. Thus, both the ASHLLC and ASHLLEM schemes can be used as reliable methods for hypersonic heating computations.