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High‐order asymptotic‐preserving schemes for linear systems: Application to the Goldstein–Taylor equations
Author(s) -
Chalons Christophe,
Turpault Rodolphe
Publication year - 2019
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22363
Subject(s) - mathematics , limit (mathematics) , taylor series , simple (philosophy) , diffusion , asymptotology , work (physics) , asymptotic analysis , order (exchange) , asymptotic expansion , reduction (mathematics) , scheme (mathematics) , method of matched asymptotic expansions , mathematical analysis , differential equation , geometry , mechanical engineering , philosophy , physics , epistemology , finance , engineering , economics , thermodynamics
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.