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Asymptotic‐preserving Godunov‐type numerical schemes for hyperbolic systems with stiff and nonstiff relaxation terms
Author(s) -
Berthon C.,
Chalons C.,
Turpault R.
Publication year - 2013
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.21749
Subject(s) - mathematics , relaxation (psychology) , type (biology) , scheme (mathematics) , operator (biology) , mathematical analysis , psychology , social psychology , ecology , biochemistry , chemistry , repressor , gene , transcription factor , biology
We devise a new class of asymptotic‐preserving Godunov‐type numerical schemes for hyperbolic systems with stiff and nonstiff relaxation source terms governed by a relaxation time ε. As an alternative to classical operator‐splitting techniques, the objectives of these schemes are twofold: first, to give accurate numerical solutions for large, small, and in‐between values of ε and second, to make optional the choice of the numerical scheme in the asymptotic regime ε tends to zero. The latter property may be of particular interest to make easier and more efficient the coupling at a fixed spatial interface of two models involving very different values of ε. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013