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arXiv · 2311.03581

Numerical schemes for coupled systems of nonconservative hyperbolic equations

Niklas Kolbe·Michael Herty·Siegfried Müller
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Abstract

A new linear relaxation system for nonconservative hyperbolic systems is introduced, in which a nonlocal source term accounts for the nonconservative product of the original system. Using an asymptotic analysis the relaxation limit and its stability are investigated. It is shown that the path-conservative Lax-Friedrichs scheme arises from a discrete limit of an implicit-explicit scheme for the relaxation system. The relaxation approach is further employed to couple two nonconservative systems at a static interface. A coupling strategy motivated from conservative Kirchhoff conditions is introduced and a corresponding Riemann solver provided. A fully discrete scheme for coupled nonconservative products is derived and studied in terms of path-conservation. Numerical experiments applying the approach to a coupled model of vascular blood flow are presented.

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Niklas Kolbe, Michael Herty, Siegfried Müller. 2023-11-06. Numerical schemes for coupled systems of nonconservative hyperbolic equations. https://arxiv.org/abs/2311.03581

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