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arXiv · 2503.01010

Coupled general Riemann problems for the Euler equations

Zhifang Du·Aleksey Sikstel
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Abstract

We introduce a novel method for systems of conservation laws coupled at a sharp interface based on generalized Riemann problems. This method yields a piecewise-linear in time approximation of the solution at the interface, thus, descynchronising the solvers for the coupled systems. We apply this framework to a problem of compressible Euler equations coupled via a gas generator and prove its solvability. Finally, we conduct numerical experiments and show that our algorithm performs at correct convergence rates.

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Zhifang Du, Aleksey Sikstel. 2025-03-02. Coupled general Riemann problems for the Euler equations. https://arxiv.org/abs/2503.01010

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