×

zbMATH — the first resource for mathematics

One-step hybrid remapping algorithm for multi-material arbitrary Lagrangian-Eulerian methods. (English) Zbl 1323.74108
Summary: In this paper, a new flux-based one-step hybrid remapping method for multi-material arbitrary Lagrangian-Eulerian (ALE) approach is introduced. In the vicinity of material interfaces, the swept region is intersected with pure material polygons in the Lagrangian mesh to construct the material fluxes. Far from interfaces, the fluxes are constructed in a standard swept-region manner without intersections. This method is conservative, second-order accurate and linearity-preserving (in the case of straight material interfaces), and faster than method based on intersections, as shown on selected numerical examples.

MSC:
74S30 Other numerical methods in solid mechanics (MSC2010)
Software:
CHIC; KULL
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Ahn, H.T.; Shashkov, M., Multi-material interface reconstruction on generalized polyhedral meshes, Journal of computational physics, 226, 2, 2096-2132, (2007) · Zbl 1388.76232
[2] P. Anninos, Kull ALE: I. Unstructured mesh advection, interface capturing, and multiphase 2T RHD with material interfaces, Technical report UCRL-ID-147297-PT-1, Lawrence Livermore National Laboratory, 2002.
[3] P. Anninos, Multiphase advection and radiation diffusion with material interfaces on unstructured meshes, Technical report UCRL-JC-150129, Lawrence Livermore National Laboratory, 2002.
[4] Barth, T.J., Numerical methods for gasdynamic systems on unstructured meshes, () · Zbl 0969.76040
[5] Berndt, M.; Breil, J.; Galera, S.; Kucharik, M.; Maire, P.-H.; Shashkov, M., Two step hybrid remapping (conservative interpolation) for multimaterial arbitrary Lagrangian-Eulerian methods, Journal of computational physics, 230, 17, 6664-6687, (2010) · Zbl 1408.65077
[6] Breil, J.; Galera, S.; Maire, P.-H., Multi-material ALE computation in inertial confinement fusion code CHIC, Computers & fluids, 46, 1, 161-167, (2011) · Zbl 1433.76190
[7] Colella, Phillip, Multidimensional upwind methods for hyperbolic conservation laws, Journal of computational physics, 87, 1, 171-200, (1990) · Zbl 0694.65041
[8] Dukowicz, J.K.; Baumgardner, J.R., Incremental remapping as a transport/advection algorithm, Journal of computational physics, 160, 1, 318-335, (2000) · Zbl 0972.76079
[9] Dukowicz, J.K.; Kodis, J.W., Accurate conservative remapping (rezoning) for arbitrary Lagrangian-Eulerian computations, SIAM journal of scientific and statistical computing, 8, 3, 305-321, (1987) · Zbl 0644.76085
[10] Dyadechko, V.; Shashkov, M., Reconstruction of multi-material interfaces from moment data, Journal of computational physics, 227, 11, 5361-5384, (2008) · Zbl 1220.76048
[11] Farrell, P.E.; Piggott, M.D.; Pain, C.C.; Gorman, G.J.; Wilson, C.R., Conservative interpolation between unstructured meshes via supermesh construction, Computer methods in applied mechanics and engineering, 198, 33-36, 2632-2642, (2009) · Zbl 1228.76105
[12] Galera, S.; Maire, P.-H.; Breil, J., A two-dimensional unstructured cell-centered multi-material ALE scheme using VOF interface reconstruction, Journal of computational physics, 229, 16, 5755-5787, (2010) · Zbl 1346.76105
[13] Garimella, R.; Kucharik, M.; Shashkov, M., An efficient linearity and bound preserving conservative interpolation (remapping) on polyhedral meshes, Computers & fluids, 36, 2, 224-237, (2007) · Zbl 1177.76346
[14] Ph. Hoch, Mesh quality and conservative projection in Lagrangian compressible hydrodynamic, in: Numerical Methods for Multi-material Fluid Flows, Prague. <http://www-troja.fjfi.cvut.cz/multimat07/presentations/tuesday/Hoch.pdf>, 2007.
[15] Ph. Hoch, An arbitrary Lagrangian-Eulerian strategy to solve compressible fluid flows, Technical report, CEA. HAL: hal-00366858. Available at: <http://hal.archives-ouvertes.fr/docs/00/36/68/58/PDF/ale2d.pdf>, 2009.
[16] Kucharik, M.; Breil, J.; Galera, S.; Maire, P.-H.; Berndt, M.; Shashkov, M., Hybrid remap for multi-material ALE, Computers & fluids, 46, 1, 293-297, (2011) · Zbl 1433.76133
[17] Kucharik, M.; Garimella, R.V.; Schofield, S.P.; Shashkov, M.J., A comparative study of interface reconstruction methods for multi-material ALE simulations, Journal of computational physics, 229, 7, 2432-2452, (2010) · Zbl 1423.76343
[18] Kucharik, M.; Shashkov, M., Extension of efficient, swept-integration based conservative remapping method for meshes with changing connectivity, International journal for numerical methods in fluids, 56, 8, 1359-1365, (2008) · Zbl 1384.65018
[19] M. Kucharik, M. Shashkov. Conservative multi-material remap for staggered discretization, in preparation. · Zbl 1349.76493
[20] Kucharik, M.; Shashkov, M., Flux-based approach for conservative remap of multi-material quantities in 2D arbitrary Lagrangian-Eulerian simulations, (), 623-631 · Zbl 1246.76103
[21] Kucharik, M.; Shashkov, M.; Wendroff, B., An efficient linearity-and-bound-preserving remapping method, Journal of computational physics, 188, 2, 462-471, (2003) · Zbl 1022.65009
[22] Lauritzen, P.H.; Erath, Ch.; Mittal, R., On simplifying ‘incremental remap’-based transport schemes, Journal of computational physics, (2011) · Zbl 1408.76384
[23] Loubere, R.; Shashkov, M., A subcell remapping method on staggered polygonal grids for arbitrary-Lagrangian-Eulerian methods, Journal of computational physics, 209, 1, 105-138, (2005) · Zbl 1329.76236
[24] Margolin, L.; Shashkov, M., Using a curvilinear grid to construct symmetry-preserving discretizations for Lagrangian gas dynamics, Journal of computational physics, 149, 2, 389-417, (1999) · Zbl 0936.76057
[25] Margolin, L.G.; Shashkov, M., Second-order sign-preserving conservative interpolation (remapping) on general grids, Journal of computational physics, 184, 1, 266-298, (2003) · Zbl 1016.65004
[26] Menon, S.; Schmidt, D.P., Conservative interpolation on unstructured polyhedral meshes: an extension of the supermesh approach to cell-centered finite-volume variables, Computer methods in applied mechanics and engineering, 200, 41-44, 2797-2804, (2011) · Zbl 1230.76034
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.