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A Third Order Adaptive ADER Scheme for One Dimensional Conservation Laws
Gu, Yaguang1; Hu, Guanghui1,2
2017-09
Source PublicationCOMMUNICATIONS IN COMPUTATIONAL PHYSICS
ISSN1815-2406
Volume22Issue:3Pages:829-851
Abstract

We introduce a third order adaptive mesh method to arbitrary high order Godunov approach. Our adaptive mesh method consists of two parts, i.e., meshredistribution algorithm and solution algorithm. The mesh-redistribution algorithm is derived based on variational approach, while a newsolution algorithmis developed to preserve high order numerical accuracywell. The feature of proposed AdaptiveADER scheme includes that 1). all simulations in this paper are stable for large CFL number, 2). third order convergence of the numerical solutions is successfully observed with adaptive mesh method, and 3). high resolution and non-oscillatory numerical solutions are obtained successfully when there are shocks in the solution. A variety of numerical examples show the feature well.

KeywordAder Scheme Adaptivemeshmethod Finite Volumemethod Weno Reconstruction Hyperbolic Equations
DOI10.4208/cicp.OA-2016-0088
URLView the original
Indexed BySCIE
Language英语
WOS Research AreaPhysics
WOS SubjectPhysics, Mathematical
WOS IDWOS:000404993500010
PublisherGLOBAL SCIENCE PRESS
The Source to ArticleWOS
Fulltext Access
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Cited Times [WOS]:2   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionDEPARTMENT OF MATHEMATICS
Affiliation1.Univ Macau, Dept Math, Taipa, Macao, Peoples R China
2.UM Zhuhai Res Inst, Zhuhai, Guangdong, Peoples R China
First Author AffilicationUniversity of Macau
Recommended Citation
GB/T 7714
Gu, Yaguang,Hu, Guanghui. A Third Order Adaptive ADER Scheme for One Dimensional Conservation Laws[J]. COMMUNICATIONS IN COMPUTATIONAL PHYSICS,2017,22(3):829-851.
APA Gu, Yaguang,&Hu, Guanghui.(2017).A Third Order Adaptive ADER Scheme for One Dimensional Conservation Laws.COMMUNICATIONS IN COMPUTATIONAL PHYSICS,22(3),829-851.
MLA Gu, Yaguang,et al."A Third Order Adaptive ADER Scheme for One Dimensional Conservation Laws".COMMUNICATIONS IN COMPUTATIONAL PHYSICS 22.3(2017):829-851.
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