Asymptotic-preserving schemes for the initial-boundary value problem of hyperbolic relaxation systems
Numerical Analysis
2025-05-29 v1 Numerical Analysis
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.
Keywords
Cite
@article{arxiv.2505.22656,
title = {Asymptotic-preserving schemes for the initial-boundary value problem of hyperbolic relaxation systems},
author = {Yizhou Zhou},
journal= {arXiv preprint arXiv:2505.22656},
year = {2025}
}