Solution Reconstruction on Unstructured Tetrahedral Meshes Using P1 -Conservative Interpolation (Advances in Applied Mathematics and Mechanics, 2018)
This paper extends an algorithm of P1-conservative interpolation on triangularmeshes to tetrahedral meshes and thus constructs an approach of solution reconstructionfor three-dimensional problems. The conservation property is achievedby local mesh intersection and the mass of a tetrahedron of the current mesh is calculatedby the integral on its intersection with the background mesh. For each currenttetrahedron, the overlapped background tetrahedrons are detected efficiently. A meshintersection algorithm is proposed to construct the intersection of a current tetrahedronwith the overlapped background tetrahedron and mesh the intersection regionby tetrahedrons. A localization algorithm is employed to search the host units in backgroundmesh for each vertex of the current mesh. In order to enforce the maximumprinciple and avoid the loss of monotonicity, correction of nodal interpolated solutionon tetrahedral meshes is given. The performance of the present solution reconstructionmethod is verified by numerical experiments on several analytic functions and thesolution of the flow around a sphere.