Time Asymptotic High Order Schemes for Dissipative BGK Hyperbolic Systems

TL;DR

This paper presents a new class of finite difference schemes for dissipative BGK hyperbolic systems that improve accuracy over time, especially for small perturbations, with demonstrated superior performance in numerical tests.

Contribution

Introduction of time-asymptotic high order schemes based on upwind approximation for dissipative BGK hyperbolic systems, with proven decay estimates and enhanced long-term accuracy.

Findings

Schemes are increasingly accurate for large times

Numerical tests confirm better performance

Effective for small perturbations of constant states

Abstract

We introduce a new class of finite differences schemes to approximate one dimensional dissipative semilinear hyperbolic systems with a BGK structure. Using precise analytical time-decay estimates of the local truncation error, it is possible to design schemes, based on the standard upwind approximation, which are increasingly accurate for large times when approximating small perturbations of constant asymptotic states. Numerical tests show their better performances with respect to those of other schemes.