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On the optimization of flux limiter schemes for hyperbolic conservation laws
Author(s) -
Breuß Michael,
Dietrich Dominik
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.21736
Subject(s) - smoothness , monotone polygon , limiter , mathematics , conservation law , flux limiter , partial differential equation , hyperbolic partial differential equation , basis (linear algebra) , flux (metallurgy) , partial derivative , method of characteristics , mathematical analysis , computer science , geometry , telecommunications , materials science , metallurgy
A classic strategy to obtain high‐quality discretizations of hyperbolic partial differential equations is to use flux limiter (FL) functions for blending two types of approximations: a monotone first‐order scheme that deals with discontinuous solution features and a higher order method for approximating smooth solution parts. In this article, we study a new approach to FL methods. Relying on a classification of input data with respect to smoothness, we associate specific basis functions with the individual smoothness notions. Then, we construct a limiter as a linear combination of the members of parameter‐dependent families of basis functions, and we explore the possibility to optimize the parameters in interesting model situations to find a corresponding optimal limiter. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013