Solution Reconstruction on Unstructured Tetrahedral Meshes Using P<sup>1</sup> -Conservative Interpolation
Year: 2016
Author: Biao Peng, Chunhua Zhou, Junqiang Ai
Advances in Applied Mathematics and Mechanics, Vol. 8 (2016), Iss. 5 : pp. 847–870
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.2015.m1087
Advances in Applied Mathematics and Mechanics, Vol. 8 (2016), Iss. 5 : pp. 847–870
Published online: 2016-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 24
Keywords: Solution reconstruction solution transfer conservative interpolation tetrahedral mesh solution interpolation mesh intersection.