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Solution Reconstruction on Unstructured Tetrahedral Meshes Using P1-Conservative Interpolation

Part of:Numerical approximation and computational geometryApproximations and expansions

Published online by Cambridge University Press:  08 July 2016

Biao Peng,
Chunhua Zhou and
Junqiang Ai
Biao Peng*
Affiliation:
Department of Aerodynamics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
Chunhua Zhou*
Affiliation:
Department of Aerodynamics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
Junqiang Ai*
Affiliation:
The First Aircraft Institute, Aviation Industry Corporation of China, Xi'an 710089, China
*
*Corresponding author. Email:pb_nuaa@126.com (B. Peng), chzhou@nuaa.edu.cn (C. H. Zhou), avic603ajq@163.com (J. Q. Ai)
*Corresponding author. Email:pb_nuaa@126.com (B. Peng), chzhou@nuaa.edu.cn (C. H. Zhou), avic603ajq@163.com (J. Q. Ai)
*Corresponding author. Email:pb_nuaa@126.com (B. Peng), chzhou@nuaa.edu.cn (C. H. Zhou), avic603ajq@163.com (J. Q. Ai)

Abstract

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This paper extends an algorithm of P1-conservative interpolation on triangular meshes to tetrahedral meshes and thus constructs an approach of solution reconstruction for three-dimensional problems. The conservation property is achieved by local mesh intersection and the mass of a tetrahedron of the current mesh is calculated by the integral on its intersection with the background mesh. For each current tetrahedron, the overlapped background tetrahedrons are detected efficiently. A mesh intersection algorithm is proposed to construct the intersection of a current tetrahedron with the overlapped background tetrahedron and mesh the intersection region by tetrahedrons. A localization algorithm is employed to search the host units in background mesh for each vertex of the current mesh. In order to enforce the maximum principle and avoid the loss of monotonicity, correction of nodal interpolated solution on tetrahedral meshes is given. The performance of the present solution reconstruction method is verified by numerical experiments on several analytic functions and the solution of the flow around a sphere.

Keywords

Solution reconstructionsolution transferconservative interpolationtetrahedral meshsolution interpolationmesh intersection

MSC classification

Secondary:41A05: Interpolation65D05: Interpolation

Information

Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 8 , Issue 5 , October 2016, pp. 847 - 870
Copyright
Copyright © Global-Science Press 2016 

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