Second-order schemes based on a relaxation system for scalar and systems of conservation laws

Christophe Chalons and Mathieu Girardin

Applied Mathematics and Computation, 2025, vol. 490, issue C

Abstract: In this paper, we propose a new class of second-order one-step time-splitting schemes for scalar and systems of conservation laws. The strategy is based on a relaxation approximation which consists in introducing a relaxation system with linearly degenerate characteristic fields to approximate the original system and deal with its nonlinearities. The numerical schemes are based on the use of arbitrarily high-order approximations of the underlying linear advection equations. Numerical evidence is proposed to illustrate the behaviour of our schemes.

Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:490:y:2025:i:c:s0096300324006349

DOI: 10.1016/j.amc.2024.129173

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