Model adaptation for hyperbolic balance laws

TL;DR

This paper introduces a model adaptation approach for hyperbolic balance laws, using a relative entropy framework to estimate errors, demonstrated through simulations of reacting fluid mixtures.

Contribution

It presents a novel model adaptation strategy for hyperbolic balance laws with error estimation based on relative entropy, applicable to chemically reacting fluids.

Findings

Effective error estimator for model adaptation.

Successful application to reacting fluid mixture simulations.

Improved accuracy with adaptive model selection.

Abstract

In this work, we devise a model adaptation strategy for a class of model hierarchies consisting of two levels of model complexity. In particular, the fine model consists of a system of hyperbolic balance laws with stiff reaction terms and the coarse model consists of a system of hyperbolic conservation laws. We employ the relative entropy stability framework to obtain an a posteriori modeling error estimator. The efficiency of the model adaptation strategy is demonstrated by conducting simulations for chemically reacting fluid mixtures in one space dimension.