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On the optimization of flux limiter schemes for hyperbolic conservation laws

Authors

  • Michael Breuß,

    Corresponding author
    1. BTU Cottbus, Institute for Applied Mathematics and Scientific Computing, HG 2.51, Platz der Deutschen Einheit 1, 03046 Cottbus, Germany
    • BTU Cottbus, Institute for Applied Mathematics and Scientific Computing, HG 2.51, Platz der Deutschen Einheit 1, 03046 Cottbus, Germany
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  • Dominik Dietrich

    1. DFKI Bremen, MZH 3120, Bibliothekstraße 1, 28359 Bremen, Germany
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Abstract

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

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