New Low-Dissipation Central-Upwind Schemes. Part II

TL;DR

This paper introduces a simple modification to low-dissipation central-upwind schemes that effectively removes oscillations near boundaries, improving solution quality without sacrificing resolution.

Contribution

It proposes a systematic modification to LDCU schemes that eliminates boundary oscillations while maintaining high resolution.

Findings

Elimination of boundary oscillations in LDCU schemes

Preservation of high resolution of contact waves

Minimal impact on overall solution quality

Abstract

The low-dissipation central-upwind (LDCU) schemes have been recently introduced in [A. Kurganov and R. Xin, J. Sci. Comput., 96 (2023), Paper No. 56] as a modification of the central-upwind (CU) schemes from [{\sc A. Kurganov and C. T. Lin, Commun. Comput. Phys., 2 (2007), pp. 141-163}]. The LDCU schemes achieve much higher resolution of contact waves and many (two-dimensional) structures resulting from complicated wave interaction. However, the LDCU schemes sometimes produce more oscillatory results compared with the CU schemes, especially near the computational domain boundaries. In this paper, we propose a very simple -- yet systematic -- modification of the LDCU schemes, which completely eliminates the aforementioned oscillations almost without affecting the quality of the computed solution.