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Solution Reconstruction on Unstructured Tetrahedral Meshes Using P1-Conservative Interpolation

Part of: Numerical approximation and computational geometry Approximations 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:[email protected] (B. Peng), [email protected] (C. H. Zhou), [email protected] (J. Q. Ai)
*Corresponding author. Email:[email protected] (B. Peng), [email protected] (C. H. Zhou), [email protected] (J. Q. Ai)
*Corresponding author. Email:[email protected] (B. Peng), [email protected] (C. H. Zhou), [email protected] (J. Q. Ai)
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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.

Keywords

Solution reconstructionsolution transferconservative interpolationtetrahedral meshsolution interpolationmesh intersection

MSC classification

Secondary: 41A05: Interpolation 65D05: Interpolation
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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References

[1]Jiao, X. and Heath, M., Common-refinement-based data transfer between non-matching meshes in multiphysics simulations, Int. J. Numer. Methods Eng., 61(14) (2004), pp. 2402–2427.Google Scholar
[2]Ringler, T. and Randall, D., A potential entropy and energy conserving numerical scheme for solution of the shallow-water equations on a geodesic grid, Monthly Weather Review, 130(5) (2002), pp. 1397–1410.Google Scholar
[3]Thuburn, J., Some conservation issues for the dynamical cores of NWP and climate models, J. Comput. Phys., 227(7) (2007), pp. 3715–3730.Google Scholar
[4]Cullen, M., Modeling atmospheric flows, Acta Numerica, 16 (2007), pp. 67–154.Google Scholar
[5]Alauzet, F. and Mehrenberger, M., P1-conservative solution interpolation on unstructured triangular meshes, Int. J. Numer. Methods Eng., 84 (2010), pp. 1552–1588.Google Scholar
[6]Alauzet, F., Frey, P., George, P. and Mohammadi, B., 3D transient fixed point mesh adaptation for time-dependent problems: application to CFD simulations, J. Comput. Phys., 222 (2007), pp. 592–623.Google Scholar
[7]Dukowicz, J. and Kodis, J., Accurate conservative remapping (rezoning) for arbitrary Lagrangian-Eulerian computations, SIAM J. Sci. Statist. Comput., 8(3) (1987), pp. 305–321.Google Scholar
[8]Garimella, R., Kucharik, M. and Shashkov, M., An efficient linearity and bound preserving conservative interpolation (remapping) on polyhedral meshes, Comput. Fluids, 36(2) (2007), pp. 224–237.Google Scholar
[9]Margolin, L. and Shashkov, M., Second-order sign-preserving conservative interpolation (remapping) on general grids, J. Comput. Phys., 184(1) (2003), pp. 266–298.Google Scholar
[10]Jones, P. W., First- and second-order conservative remapping schemes for grids in spherical coordinates, Monthly Weather Review, 127(9) (1999), pp. 2204–2210.Google Scholar
[11]Cheng, J. and Shu, C. W., A high order accurate conservative remapping method on staggered meshes, Appl. Numer. Math., 58(7) (2008), pp. 1042–1060.Google Scholar
[12]Grandy, J., Conservative remapping and regions overlays by intersecting polyhedral, J. Comput. Phys., 148(2) (1999), pp. 433–466.Google Scholar
[13]Dukowicz, J. K., Conservative rezoning (remapping) for general quadrilateral meshes, J. Comput. Phys., 54 (1984), pp. 411–424.Google Scholar
[14]Geuzaine, C., Meys, B., Henrotte, F., Dular, P. and Legros, W., A Galerkin projection method for mixed finite elements, IEEE Transactions on Magnetics, 35(3) (1999), pp. 1438–1441.Google Scholar
[15]Farrell, P., Piggott, M., Pain, C. and Gorman, G., Conservative interpolation between unstructured meshes via supermesh construction, Comput. Methods Appl. Mech. Eng., 198 (2009), pp. 2632–2642.Google Scholar
[16]Farrell, P. E. and Maddison, J. R., Conservative interpolation between volume meshes by local Galerkin projection, Comput. Methods Appl. Mech. Eng., 200 (2011), pp. 89–100.Google Scholar
[17]Zhou, C. H. and Ai, J. Q., Mesh adaptation for simulation of unsteady flow with moving immersed boundaries, Int. J. Numer. Methods Fluids, 72 (2013), pp. 453–477.Google Scholar
[18]Frey, P. and George, P., Mesh Generation, Application to Finite Elements (2nd edn), ISTE Ltd and Wiley: New York, 2008.Google Scholar
[19]Löhner, R., Applied CFD Techniques, An Introduction Based on Finite Element Methods, Wiley: New York, 2001.Google Scholar
[20]Preparata, F. P. and Shamos, M. I., Computational Geometry: An Introduction, Second ed., Springer, 1985.Google Scholar
[21]Seidel, R., Convex Hull Computations, in: Goodman, J. E. and óRourke, J. (Eds.), Handbook of Discrete and Computational Geometry, Chapman & Hall/CRC, 2004, pp. 495–512.Google Scholar