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

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.

Figures (20)

• Figure 1: Results of Sod shock tube problem
• Figure 2: Plot of maximum real eigenvalues vs upstream Mach number for the HLL-family schemes
• Figure 3: Boundary layer profile for $M_{\infty}=0.20$ laminar flow over a flat plate computed by the HLLE, HLL-CPS and HLLEM schemes
• Figure 4: Distribution of the eigenvalues of $\mathbf{S}$ in the complex plane for the proposed HLLEM-FP and HLL-CPS-FP Schemes for an upstream Mach number of 7.0
• Figure 5: Plot of maximum real eigenvalue vs upstream Mach number for the proposed HLLEM-FP and HLL-CPS-FP schemes