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

Numerical Methods for Partial Differential Equations, vol. 42

Abstract

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.

Authors 2

1. Shaoshuai Chu Aachen Department of Mathematics

   RWTH Aachen University

   Affiliation as printed

   Department of Mathematics RWTH Aachen University Aachen Germany

2. Michaël Herty Aachen Department of Mathematics

   RWTH Aachen University · University of Pretoria

   Affiliation as printed

   Department of Mathematics RWTH Aachen University Aachen Germany

   Department of Mathematics and Applied Mathematics University of Pretoria Hatfield, Pretoria South Africa