Asymptotic-preserving schemes for the initial-boundary value problem of hyperbolic relaxation systems

Yizhou Zhou

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arXiv · 2505.22656

Asymptotic-preserving schemes for the initial-boundary value problem of hyperbolic relaxation systems

Yizhou Zhou

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Abstract

In this work, we present a numerical method for the initial-boundary value problem (IBVP) of first-order hyperbolic systems with source terms. The scheme directly solves the relaxation system using a relatively coarse mesh and captures the equilibrium behavior quite well, even in the presence of boundary layers. This method extends the concept of asymptotic-preserving schemes from initial-value problems to IBVPs. Moreover, we apply this idea to design a unified numerical scheme for the interface problem of relaxation systems.

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Yizhou Zhou. 2025-05-28. Asymptotic-preserving schemes for the initial-boundary value problem of hyperbolic relaxation systems. https://arxiv.org/abs/2505.22656

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