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

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  • Chalons, Christophe
  • Girardin, Mathieu

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.

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  • Chalons, Christophe & Girardin, Mathieu, 2025. "Second-order schemes based on a relaxation system for scalar and systems of conservation laws," Applied Mathematics and Computation, Elsevier, vol. 490(C).
    • Handle: RePEc:eee:apmaco:v:490:y:2025:i:c:s0096300324006349
    DOI: 10.1016/j.amc.2024.129173
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