Conservative interpolation between unstructured meshes via supermesh construction

Computer Methods in Applied Mechanics and Engineering

Volumn 198, Issue 33-36, 2009, Pages 2632-2642

  Farrell, P E ^a   Piggott, M D ^a   Pain, C C ^a   Gorman, G J ^a   Wilson, C R ^a  

^a IMPERIAL COLLEGE LONDON   (United Kingdom)

Author keywords

Conservation; Delaunay triangulation; Interpolation; Mesh adaptivity; Supermesh

Indexed keywords

ARBITRARY ANISOTROPY; BASIS FUNCTIONS; COMPUTATIONAL COSTS; CONSERVATIVE INTERPOLATION; DELAUNAY TRIANGULATION; GEOMETRIC FLEXIBILITY; INTERPOLATION ERROR; MESH ADAPTIVITY; NUMERICAL SIMULATION; SUPERMESH; TRACER CONCENTRATION; UNSTRUCTURED MESHES;

COST REDUCTION; TRIANGULATION;

INTERPOLATION;

EID: 65849449038     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2009.03.004     Document Type: Article

References (44)

1. Alauzet F. High-order methods and mesh adaptation for Euler equations. International Journal for Numerical Methods in Fluids 58 (2008) 1069-1076
2. Arakawa A., and Lamb V.R. A potential enstrophy and energy conserving scheme for the shallow water equations. Monthly Weather Review 109 1 (1981) 18-36
3. Babuška I., and Rheinboldt W.C. Error estimates for adaptive finite element computations. SIAM Journal on Numerical Analysis 15 4 (1978) 736-754
4. Balay S., Gropp W.D., McInnes L.C., and Smith B.F. Efficient management of parallelism in object oriented numerical software libraries. In: Arge E., Bruaset A.M., and Langtangen H.P. (Eds). Modern Software Tools in Scientific Computing (1997), Birkhäuser Press 163-202
5. D.M. Bradley, 2005. Counting the positive rationals: A brief survey. URL .
6. Chesshire G., and Henshaw W.D. A scheme for conservative interpolation on overlapping grids. SIAM Journal on Scientific Computing 15 (1994) 819
7. Chew P.L. Constrained Delaunay triangulations. Algorithmica 4 1 (1989) 97-108
8. Chew P.L. Guaranteed-quality mesh generation for curved surfaces. Proceedings of the ninth annual symposium on Computational geometry (1993), ACM, New York, NY, USA 274-280
9. Cullen M. Modelling atmospheric flows. Acta Numerica 16 (2007) 67-154
10. Dukowicz J.K., and Kodis J.W. Accurate conservative remapping (rezoning) for arbitrary Lagrangian-Eulerian computations. SIAM Journal on Scientific and Statistical Computing 8 (1987) 305-321
11. Dukowicz J.K. Conservative rezoning (remapping) for general quadrilateral meshes. Journal of Computational Physics 54 (1984) 411-424
12. Eisenstat S.C. Efficient implementation of a class of preconditioned conjugate gradient methods. SIAM Journal on Scientific and Statistical Computing 2 1 (1981) 1-4
13. Garimella R., Kucharik M., and Shashkov M. An efficient linearity and bound preserving conservative interpolation (remapping) on polyhedral meshes. Computers and Fluids 36 2 (2007) 224-237
14. P.L. George, H. Borouchaki, 1998. Delaunay Triangulation and Meshing: Application to Finite Elements, Hermes.
15. Grandy J. Conservative remapping and region overlays by intersecting arbitrary polyhedra. Journal of Computational Physics 148 2 (1999) 433-466
16. Hestenes M.R., and Stiefel E. Methods of conjugate gradients for solving linear systems. Journal of Research of the National Bureau of Standards 49 6 (1952) 409-436
17. Hirt C.W., Amsden A.A., and Cook J.L. An arbitrary Lagrangian-Eulerian computing method for all flow speeds. Journal of Computational Physics 14 (1974) 227
18. Iske A., and Käser M. Conservative semi-Lagrangian advection on adaptive unstructured meshes. Numerical Methods for Partial Differential Equations 20 (2004) 338-411
19. Jiao X., and Heath M.T. Common-refinement-based data transfer between non-matching meshes in multiphysics simulations. International Journal for Numerical Methods in Engineering 61 (2004) 2402-2427
20. Kucharik M., and Shashkov M. Extension of efficient, swept-integration-based conservative remapping method for meshes with changing connectivity. International Journal for Numerical Methods in Fluids 56 (2007) 1359-1365
21. Lee D.T., and Lin A.K. Generalized Delaunay triangulation for planar graphs. Discrete and Computational Geometry 1 1 (1986) 201-217
22. Löhner R. Robust, vectorized search algorithms for interpolation on unstructured grids. Journal of Computational Physics 118 2 (1995) 380-387
23. Margolin L.G., and Shashkov M. Second-order sign-preserving conservative interpolation (remapping) on general grids. Journal of Computational Physics 184 1 (2003) 266-298
24. Mount D.M. Geometric intersection. In: Goodman J.E., and O'Rourke J. (Eds). Handbook of discrete and computational geometry (1997), CRC Press, Inc., Boca Raton, FL, USA 615-630
25. Pain C.C., Gomes J., Eaton M., de Oliveira C., and Goddard A. A model of heat transfer dynamics of coupled multiphase-flow and neutron-radiation: application to a nuclear fluidized bed reactor. International Journal of Numerical Methods for Heat and Fluid Flow 15 8 (2005) 765-807
26. Pain C., Umpleby A., de Oliveira C., and Goddard A. Tetrahedral mesh optimisation and adaptivity for steady-state and transient finite element calculations. Computer Methods in Applied Mechanics and Engineering 190 29-30 (2001) 3771-3796
27. Phillips T.N., and Williams A.J. Conservative semi-Lagrangian finite volume schemes. Numerical Methods for Partial Differential Equations 17 (2001) 403-425
28. Piggott M.D., Gorman G.J., Pain C.C., Allison P.A., Candy A.S., Martin B.T., and Wells M.R. A new computational framework for multi-scale ocean modelling based on adapting unstructured meshes. International Journal for Numerical Methods in Fluids 56 8 (2008) 1003-1015
29. Rashid M.M. Material state remapping in computational solid mechanics. International Journal for Numerical Methods in Engineering 5 (2002) 431-450
30. Ringler T.D., and Randall D.A. A potential enstrophy and energy conserving numerical scheme for solution of the shallow-water equations on a geodesic grid. Monthly Weather Review 130 5 (2002) 1397-1410
31. Rudman M. Volume-tracking methods for interfacial flow calculations. International Journal for Numerical Methods in Fluids 24 7 (1997) 671-691
32. Ruppert J. A Delaunay refinement algorithm for quality 2-dimensional mesh generation. Journal of Algorithms 18 3 (1995) 548-585
33. Rüter M., Korotov S., and Steenbock C. Goal-oriented error estimates based on different FE-spaces for the primal and the dual problem with applications to fracture mechanics. Computational Mechanics 39 6 (2007) 787-797
34. Sadourny R. The dynamics of finite-difference models of the shallow-water equations. Journal of the Atmospheric Sciences 32 4 (1975) 680-689
35. Scroggs J.S., and Semazzi F.H.M. A conservative semi-Lagrangian method for multidimensional fluid dynamics applications. Numerical Methods for Partial Differential Equations 11 (1995) 445-452
36. Shewchuk J.R. Triangle: engineering a 2D quality mesh generator and Delaunay triangulator. Applied Computational Geometry: Towards Geometric Engineering 1148 (1996) 203-222
37. Shewchuk J.R. Delaunay refinement algorithms for triangular mesh generation. Computational Geometry: Theory and Applications 22 1-3 (2002) 21-74
38. J. Slingo, K. Bates, N. Nikiforakis, M.D. Piggott, M. Roberts, L. Shaffrey, I. Stevens, P. Vidale, H. Weller, Developing the next generation climate system models: challenges and achievements. Philosophical Transactions of the Royal Society A 367 (2009) 815-831.
39. Smolarkiewicz P.K., and Rasch P.J. Monotone advection on the sphere: an Eulerian versus semi-Lagrangian approach. Journal of the Atmospheric Sciences 48 6 (1991) 793-810
40. Staniforth A., and Côté J. Semi-Lagrangian integration schemes for atmospheric models: a review. Monthly Weather Review 119 9 (1991) 2206-2223
41. Thuburn J. Some conservation issues for the dynamical cores of NWP and climate models. Journal of Computational Physics 227 7 (2008) 3715-3730
42. Vasilevskii Y., and Lipnikov K. An adaptive algorithm for quasioptimal mesh generation. Computational Mathematics and Mathematical Physics 39 9 (1999) 1468-1486
43. C.R. Wilson, 2009. Modelling multiple-material flows on adaptive unstructured meshes. Ph.D. thesis, Imperial College London, London, UK.
44. Zienkiewicz O.C., and Taylor R.L. The finite element method. Fluid Dynamics vol. III (2000), Butterworth-Heinemann