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arXiv · 2601.11172

Discontinuous Galerkin schemes for multi-dimensional coupled hyperbolic systems

Niklas Kolbe·Siegfried Müller·Aleksey Sikstel
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Abstract

A novel class of Runge-Kutta discontinuous Galerkin schemes for coupled systems of conservation laws in multiple space dimensions that are separated by a fixed sharp interface is introduced. The schemes are derived from a relaxation approach and a local projection and do not require expensive solutions of nonlinear half-Riemann problems. The underlying Jin-Xin relaxation involves a problem specific modification of the coupling condition at the interface, for which a simple construction algorithm is presented. The schemes are endowed with higher order time discretization by means of strong stability preserving Runge-Kutta methods. These are derived from an asymptotic preserving implicit-explicit treatment of the coupled relaxation system taken to the discrete relaxation limit. In a case study the application to a multi-dimensional fluid-structure coupling problem employing the compressible Euler equations and a linear elastic model is discussed.

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Niklas Kolbe, Siegfried Müller, Aleksey Sikstel. 2026-01-16. Discontinuous Galerkin schemes for multi-dimensional coupled hyperbolic systems. https://arxiv.org/abs/2601.11172

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