Enhanced HLLEM and HLL-CPS schemes for all Mach number flows based using anti-diffusion coefficients

TL;DR

This paper enhances HLLEM and HLL-CPS schemes for Euler equations to improve accuracy and stability across all Mach numbers by introducing anti-diffusion modifications, validated through stability analysis and numerical tests.

Contribution

The paper introduces novel modifications to HLLEM and HLL-CPS schemes, improving their robustness and accuracy for all Mach number flows, including low Mach regimes.

Findings

Enhanced schemes are stable and free from shock instabilities at high speeds.

Improved schemes accurately resolve low Mach number flow features.

Numerical tests confirm robustness and effectiveness of the proposed modifications.

Abstract

This paper compares the HLLEM and HLL-CPS schemes for Euler equations and proposes improvements for all Mach number flows. Enhancements to the HLLEM scheme involve adding anti-diffusion terms in the face normal direction and modifying anti-diffusion coefficients for linearly degenerate waves near shocks. The HLL-CPS scheme is improved by adjusting anti-diffusion coefficients for the face normal direction and linearly degenerate waves. Matrix stability, linear perturbation, and asymptotic analyses demonstrate the robustness of the proposed schemes and their ability to capture low Mach flow features. Numerical tests confirm that the schemes are free from shock instabilities at high speeds and accurately resolve low Mach number flow features.