A low Diffusion HLL-CPS Scheme for all Mach number flows

TL;DR

This paper introduces a low diffusion HLL-CPS scheme that accurately captures flow features across all Mach numbers by reducing numerical dissipation and improving robustness at low and high Mach regimes.

Contribution

The paper develops a novel low diffusion HLL-CPS scheme with asymptotic correctness and enhanced shock robustness, addressing limitations of existing schemes at low Mach numbers.

Findings

Correct scaling of pressure at low Mach numbers

Significant reduction in numerical dissipation

Improved robustness for strong shocks

Abstract

A low diffusion version of the HLL-CPS scheme for resolving the shear layers and the flow features at low Mach numbers is presented here. The low diffusion HLL-CPS scheme is obtained by reconstructing the velocities at the cell interface with the face normal Mach number and a pressure function. Asymptotic analysis of the modified scheme shows a correct scaling of the pressure at low Mach numbers and a significant reduction in numerical dissipation. The robustness of the HLL-CPS scheme for strong shock is improved by reducing the contribution of the contact wave in the vicinity of the shock. The improvement in robustness for strong shock is demonstrated analytically through linear perturbation and matrix stability analyses. A set of numerical test cases are solved to demonstrate the efficacy of the proposed scheme over a wide range of Mach numbers.