Conservative interpolation on unstructured polyhedral meshes: an extension of the supermesh approach to cell-centered finite-volume variables. (English) Zbl 1230.76034
Summary: A method is presented for conservatively transferring, or remapping, cell-centered variable fields from one mesh to another with second-order accuracy. The method is generally applicable to any polyhedral source or target mesh. Like the work of P. E. Farrell et al. [ibid. 198, No. 33–36, 2632–2642 (2009; Zbl 1228.76105)], which was designed for finite-element computations, the proposed methodology uses a logical supermesh consisting of the intersections of polyhedra from both meshes. The resulting transfer process is well-suited for finite-volume methods that rely on cell-centered variables. The accuracy and efficacy of the new remapping process is demonstrated with numerical experiments and a computational fluid dynamics test.
MSC:
| 76M12 | Finite volume methods applied to problems in fluid mechanics |
| 76R99 | Diffusion and convection |
Keywords:
remapping; supermesh; conservative interpolation; mesh adaptation; finite volume method; polyhedral meshesCitations:
Zbl 1228.76105References:
| [1] | Farrell, P.; Piggott, M.; Pain, C.; Gorman, G.; Wilson, C., Conservative interpolation between unstructured meshes via supermesh construction, Comput. Methods Appl. Mech. Engrg., 198, 33-36, 2632-2642 (2009) · Zbl 1228.76105 |
| [2] | Perot, B.; Nallapati, R., A moving unstructered staggered mesh method for the simulation of incompressible free surface flows, J. Comput. Phys., 184, 192-214 (2003) · Zbl 1118.76307 |
| [3] | Dai, M.; Schmidt, D. P., Adaptive tetrahedral meshing in free-surface flow, J. Comput. Phys., 208, 1, 228-252 (2005) · Zbl 1114.76333 |
| [4] | F. Brusiani, G.M. Bianchi, T. Lucchini, G. D’Errico, Implementation of a Finite-Element Based Mesh Motion Technique in an Open Source CFD Code, in: ASME Conference Proceedings 2009, vol. 43406, 2009, pp. 611-624.; F. Brusiani, G.M. Bianchi, T. Lucchini, G. D’Errico, Implementation of a Finite-Element Based Mesh Motion Technique in an Open Source CFD Code, in: ASME Conference Proceedings 2009, vol. 43406, 2009, pp. 611-624. |
| [5] | Pain, C.; Umpleby, A.; de Oliveira, C.; Goddard, A., Tetrahedral mesh optimisation and adaptivity for steady-state and transient finite element calculations, Comput. Methods Appl. Mech. Engrg., 190, 3771-3796 (2001), 26 · Zbl 1008.76041 |
| [6] | Margolin, L. G.; Shashkov, M., Second-order sign-preserving conservative interpolation (remapping) on general grids, J. Comput. Phys., 184, 1, 266-298 (2003) · Zbl 1016.65004 |
| [7] | Loubère, R.; Shashkov, M. J., A subcell remapping method on staggered polygonal grids for arbitrary-Lagrangian-Eulerian methods, J. Comput. Phys., 209, 1, 105-138 (2005) · Zbl 1329.76236 |
| [8] | M. Berndt, J. Breil, S. Galera, M. Kucharik, P.-H. Maire, M. Shashkov, Two-Step Hybrid Remapping (Conservative Interpolation) for Multimaterial Arbitrary Lagrangian-Eulerian Methods, Tech. Rep., LA-UR-10-05438, Report of Los Alamos National Laboratory, Los Alamos, NM, USA, 2010.; M. Berndt, J. Breil, S. Galera, M. Kucharik, P.-H. Maire, M. Shashkov, Two-Step Hybrid Remapping (Conservative Interpolation) for Multimaterial Arbitrary Lagrangian-Eulerian Methods, Tech. Rep., LA-UR-10-05438, Report of Los Alamos National Laboratory, Los Alamos, NM, USA, 2010. · Zbl 1408.65077 |
| [9] | Kucharik, M.; Shashkov, M.; Wendroff, B., An efficient linearity-and-bound-preserving remapping method, J. Comput. Phys., 188, 2, 462-471 (2003) · Zbl 1022.65009 |
| [10] | Loubère, R.; Maire, P.-H.; Shashkov, M.; Breil, J.; Galera, S., ReALE: A reconnection-based arbitrary-Lagrangian-Eulerian method, J. Comput. Phys., 229, 12, 4724-4761 (2010) · Zbl 1305.76067 |
| [11] | J.K. Dukowicz, N. Padial, REMAP3D: a conservative three dimensional remapping code, Tech. Rep., LA-12136-MS, Report of Los Alamos National Laboratory, Los Alamos, NM, USA, 1991.; J.K. Dukowicz, N. Padial, REMAP3D: a conservative three dimensional remapping code, Tech. Rep., LA-12136-MS, Report of Los Alamos National Laboratory, Los Alamos, NM, USA, 1991. |
| [12] | Alauzet, F.; Mehrenberger, M., P1-conservative solution interpolation on unstructured triangular meshes, Int. J. Numer. Methods Engrg., 84, 13, 1552-1588 (2010) · Zbl 1202.76096 |
| [13] | Grandy, J., Conservative remapping and region overlays by intersecting arbitrary polyhedra, J. Comput. Phys., 148, 2, 433-466 (1999) · Zbl 0932.76073 |
| [14] | Garimella, R.; Kucharik, M.; Shashkov, M., An efficient linearity and bound preserving conservative interpolation (remapping) on polyhedral meshes, Comput. Fluids, 36, 2, 224-237 (2007) · Zbl 1177.76346 |
| [15] | Dukowicz, J. K., Conservative rezoning (remapping) for general quadrilateral meshes, J. Comput. Phys., 54, 3, 411-424 (1984) · Zbl 0534.76008 |
| [16] | Dukowicz, J. K.; Kodis, J. W., Accurate conservative remapping (rezoning) for arbitrary Lagrangian-Eulerian computations, SIAM J. Sci. Stat. Comput., 8, 3, 305-321 (1987) · Zbl 0644.76085 |
| [17] | Jones, P. W., First- and second-order conservative remapping schemes for grids in spherical coordinates, Mon. Weather Rev., 127, 9, 2204-2210 (1999) |
| [18] | Azarenok, B., A method for conservative remapping on hexahedral meshes, Math. Models Comput. Simul., 1, 51-63 (2009) |
| [19] | Jiao, X.; Heath, M. T., Common-refinement-based data transfer between nonmatching meshes in multiphysics simulations, Int. J. Numer. Methods Engrg., 61, 14, 2402-2427 (2004) · Zbl 1075.74711 |
| [20] | Farrell, P.; Maddison, J., Conservative interpolation between volume meshes by local Galerkin projection, Comput. Methods Appl. Mech. Engrg., 200, 1-4, 89-100 (2011) · Zbl 1225.76193 |
| [21] | H. Samet, A. Kochut, Octree approximation an compression methods, in: Proceedings First International Symposium on 3D Data Processing Visualization and Transmission, 2002.; H. Samet, A. Kochut, Octree approximation an compression methods, in: Proceedings First International Symposium on 3D Data Processing Visualization and Transmission, 2002. |
| [22] | Ahn, H.; Shashkov, M., Geometric algorithms for 3D interface reconstruction, (Brewer, M. L.; Marcum, D., Proceedings of the 16th International Meshing Roundtable (2008), Springer: Springer Berlin, Heidelberg), 405-422 · Zbl 1134.65311 |
| [23] | Eberly, D. H., 3D Game Engine Design: A Practical Approach to Real-Time Computer Graphics (2000), Morgan Kaufmann |
| [24] | Chazelle, B., An optimal algorithm for intersecting three-dimensional convex polyhedra, SIAM J. Comput., 21, 671-696 (1992), ISSN 0097-5397 · Zbl 0825.68642 |
| [25] | Farrell, P., The addition of fields on different meshes, J. Comput. Phys., 230, 9, 3265-3269 (2011) · Zbl 1218.65024 |
| [26] | Nichols, B.; Buttlar, D.; Farrell, J., Pthreads Programming (1996), O’Reilly and Associates, Inc.: O’Reilly and Associates, Inc. Sebastopol, CA, USA |
| [27] | Roe, P. L., Large scale computations in fluid mechanics. Part 2, Lect. Appl. Math., 22, 163-193 (1985) · Zbl 0665.76072 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
