A Comparative Study of Low-Dissipation Numerical Schemes for Hyperbolic Conservation Laws

TL;DR

This paper compares various low-dissipation numerical schemes for hyperbolic conservation laws, assessing their accuracy, robustness, and efficiency through extensive gas dynamics simulations to guide solver selection.

Contribution

It provides a comprehensive comparison of several low-dissipation schemes, extending them to higher orders and evaluating their performance on complex flow problems.

Findings

Low-dissipation schemes have comparable numerical dissipation levels.

Subtle differences affect wave resolution and robustness.

Guidance for choosing efficient solvers for compressible flows.

Abstract

This work provides a comparative assessment of several low-dissipation numerical schemes for hyperbolic conservation laws, highlighting their performance relative to the classical Harten-Lax-van Leer (HLL) schemes. The schemes under consideration include the classical Harten-Lax-van Leer-Contact (HLLC), the recently proposed TV flux splitting, the low-dissipation Central-Upwind (LDCU), and the local characteristic decomposition-based Central-Upwind (LCDCU) schemes. These methods are extended to higher orders of accuracy, up to the fifth order, within both finite-volume and finite-difference frameworks. A series of numerical experiments for the one- and two-dimensional Euler equations of gas dynamics are performed to evaluate the accuracy, robustness, and computational efficiency of the studied schemes. The comparison highlights the trade-offs between resolution of contact and shear waves, robustness in the presence of shocks, and computational cost. The investigated low-dissipation schemes show comparable levels of numerical dissipation, with only subtle differences appearing in selected benchmark problems. The results provide practical guidance for selecting efficient low-dissipation solvers for the simulation of complex compressible flows.