High‐order asymptotic‐preserving schemes for linear systems: Application to the Goldstein–Taylor equations. Issue 4 (21st February 2019)

• Record Type: Journal Article
• Authors: Chalons, Christophe; Turpault, Rodolphe
• Is Part Of: Numerical methods for partial differential equations. Volume 35:Issue 4(2019)
• Page Start: 1538
• Page End: 1561
• Publication Date: 2019-02-21
• Subjects: asymptotic‐preserving schemes -- diffusion limit for linear hyperbolic systems -- high order finite volumes schemes; Differential equations, Partial -- Numerical solutions -- Periodicals; 515.353
• DOI: 10.1002/num.22363
• Languages: English
• ISSNs: 0749-159X

Abstract

Abstract : In this work, we address the numerical approximation of linear systems with possibly stiff source terms which induce an asymptotic diffusion limit. More precisely, we are interested in the design of high‐order asymptotic‐preserving schemes. Our approach is based on a very simple modification of the numerical flux associated with the usual HLL scheme. This alteration can be understood as a numerical diffusion reduction technique and allows to capture the correct asymptotic behavior in the diffusion limit and to consider uniformly high‐order extensions. We more specifically consider the case of the Goldstein–Taylor model but the overall approach is shown to be easily adapted to more general systems.