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Integrated Linear Reconstruction for Finite Volume Scheme on Arbitrary Unstructured Grids
Li Chen1; Guanghui Hu2,3; Ruo Li1,4
2018-08
Source PublicationCommunications in computational physics
ISSN1815-2406
Volume24Issue:2Pages:454-480
Abstract

In [L. Chen and R. Li, Journal of Scientific Computing, Vol. 68, pp. 1172– 1197, (2016)], an integrated linear reconstruction was proposed for finite volume methods on unstructured grids. However, the geometric hypothesis of the mesh to enforce a local maximum principle is too restrictive to be satisfied by, for example, locally refined meshes or distorted meshes generated by arbitrary Lagrangian-Eulerian methods in practical applications. In this paper, we propose an improved integrated linear reconstruction approach to get rid of the geometric hypothesis. The resulting optimization problem is a convex quadratic programming problem, and hence can be solved efficiently by classical active-set methods. The features of the improved integrated linear reconstruction include that i). the local maximum principle is fulfilled on arbitrary unstructured grids, ii). the reconstruction is parameter-free, and iii). the finite volume scheme is positivity-preserving when the reconstruction is generalized to the Euler equations. A variety of numerical experiments are presented to demonstrate the performance of this method.

KeywordLinear Reconstruction Local Maximum Principle Positivity-preserving Quadratic Programming Finite Volume Method
DOI10.4208/cicp.OA-2017-0137
Language英语
WOS Research AreaPhysics
WOS SubjectPhysics, Mathematical
WOS IDWOS:000455954900007
PublisherGLOBAL SCIENCE PRESS, ROOM 3208, CENTRAL PLAZA, 18 HARBOUR RD, WANCHAI, HONG KONG 00000, PEOPLES R CHINA
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Document TypeJournal article
CollectionDEPARTMENT OF MATHEMATICS
Affiliation1.Peking Univ, Sch Math Sci, Beijing, Peoples R China
2.Univ Macau, Dept Math, Macau, Peoples R China
3.UM Zhuhai Res Inst, Zhuhai, Guangdong, Peoples R China
4.Peking Univ, LMAM, HEDPS & CAPT, Beijing, Peoples R China
Recommended Citation
GB/T 7714
Li Chen,Guanghui Hu,Ruo Li. Integrated Linear Reconstruction for Finite Volume Scheme on Arbitrary Unstructured Grids[J]. Communications in computational physics,2018,24(2):454-480.
APA Li Chen,Guanghui Hu,&Ruo Li.(2018).Integrated Linear Reconstruction for Finite Volume Scheme on Arbitrary Unstructured Grids.Communications in computational physics,24(2),454-480.
MLA Li Chen,et al."Integrated Linear Reconstruction for Finite Volume Scheme on Arbitrary Unstructured Grids".Communications in computational physics 24.2(2018):454-480.
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