Regular Article
Numerical Schemes for Hyperbolic Conservation Laws with Stiff Relaxation Terms

https://doi.org/10.1006/jcph.1996.0149Get rights and content

Abstract

Hyperbolic systems often have relaxation terms that give them a partially conservative form and that lead to a long-time behavior governed by reduced systems that are parabolic in nature. In this article it is shown by asymptotic analysis and numerical examples that semidiscrete high resolution methods for hyperbolic conservation laws fail to capture this asymptotic behavior unless the small relaxation rate is resolved by a fine spatial grid. We introduce a modification of higher order Godunov methods that possesses the correct asymptotic behavior, allowing the use of coarse grids (large cell Peclet numbers). The idea is to build into the numerical scheme the asymptotic balances that lead to this behavior. Numerical experiments on 2 × 2 systems verify our analysis.

References (0)

Cited by (198)

  • Numerical study of multiphase hyperbolic models

    2023, Journal of Computational and Applied Mathematics
    Citation Excerpt :

    These issues are addressed in the context of the so called “asymptotic preserving schemes”. Up to the authors the best knowledge, most results in this field are related to the conservative system of equations see, e.g., [13–17]. For quasi-linear barotropic version of the BN7 model, the asymptotic preserving schemes has been developed in [18].

  • The hydrodynamics of LERNA

    2022, Journal of Computational Physics
View all citing articles on Scopus
1

E-mail address: [email protected].

2

E-mail address: [email protected].

View full text