ADER schemes for three-dimensional non-linear hyperbolic systems

In this paper, we carry out the extension of the ADER approach to multidimensional non-linear systems of conservation laws. We implement non-linear schemes of up to fourth order of accuracy in both time and space. Numerical results for the compressible Euler equations illustrate the very high order...

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Bibliographic Details
Published inJournal of computational physics Vol. 204; no. 2; pp. 715 - 736
Main Authors Titarev, V.A., Toro, E.F.
Format Journal Article
LanguageEnglish
Published Elsevier Inc 10.04.2005
Subjects
ADER
Generalized Riemann problem
High-order schemes
Three space dimensions
Weighted essentially non-oscillatory
Three space dimensions
High-order schemes
Weighted essentially non-oscillatory
ADER
Generalized Riemann problem
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Summary:In this paper, we carry out the extension of the ADER approach to multidimensional non-linear systems of conservation laws. We implement non-linear schemes of up to fourth order of accuracy in both time and space. Numerical results for the compressible Euler equations illustrate the very high order of accuracy and non-oscillatory properties of the new schemes. Compared to the state-of-art finite-volume WENO schemes the ADER schemes are faster, more accurate, need less computer memory and have no theoretical accuracy barrier.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2004.10.028