×

zbMATH — the first resource for mathematics

A multi-material ReALE method with MOF interface reconstruction. (English) Zbl 1290.76094
Summary: We present a comparison of a classical arbitrary Lagrangian-Eulerian (ALE) method with a new multi-material reconnection-based arbitrary-Lagrangian-Eulerian (Re-ALE) strategy devoted to the computation of multi-material compressible fluid flows using the Moment Of Fluid (MOF) interface reconstruction. In ReALE we replace the rezoning phase of classical ALE method by a rezone where we allow the connectivity between cells of the mesh to change where rezoned grid is a polygonal mesh. Nevertheless, the ability of pure Lagrangian method to deal with multi-material problem, where mesh is aligned with material interfaces, is lost. In this work we have implemented MOF interface reconstruction on polygonal mesh in ReALE framework. This leads to a formulation that recover the Lagrangian features of following material and material interface that we lose using standard ALE methods with fixed connectivity. Some numerical examples, are used to clearly illustrate the robustness and accuracy of the new method.

MSC:
76M20 Finite difference methods applied to problems in fluid mechanics
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
76N15 Gas dynamics (general theory)
Software:
ReALE
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Aulisa, E.; Manservisi, S.; Scardovelli, R., A surface marker algorithm coupled to an area-preserving marker redistribution method for three-dimensional interface tracking, J Comput Phys, 197, 555-584, (2004) · Zbl 1079.76605
[2] Ahn, H. T.; Shashkov, M. J., Multi-material interface reconstruction on generalized polyhedral meshes, J Comput Phys, 226, 2, 2096-2132, (2007) · Zbl 1388.76232
[3] Berndt, M.; Breil, J.; Galera, S.; Kucharik, M.; Maire, P.-H.; Shashkov, M., Two-step hybrid conservative remapping for multi-material arbitrary Lagrangian-Eulerian methods, J Comput Phys, 230, 17, 6664-6687, (2011) · Zbl 1408.65077
[4] Breil, J.; Galera, S.; Maire, P.-H., A two-dimensional VOF interface reconstruction in a multi-material cell-centered ALE scheme, Int J Numer Methods Fluids, 65, 11-12, 1351-1364, (2011) · Zbl 1456.76100
[5] Dyadechko, V.; Shashkov, M., Reconstruction of multi-material interfaces from moment data, J Comput Phys, 227, 11, 5361-5384, (2008) · Zbl 1220.76048
[6] Galera, S.; Breil, J.; Maire, P.-H., A 2D unstructured multi-material cell-centered arbitrary Lagrangian-Eulerian (CCALE) scheme using MOF interface reconstruction, Comput Fluids, 46, 1, 237-244, (2011) · Zbl 1432.76215
[7] Galera, S.; Maire, P.-H.; Breil, J., A two-dimensional unstructured cell-centered multi-material ALE scheme using VOF interface reconstruction, J Comput Phys, 229, 16, 5755-5787, (2010) · Zbl 1346.76105
[8] Haas, J.-F.; Sturtevant, B., Interaction of weak shock wave with cylindrical and spherical gas inhomogeneities, J Fluid Mech, 181, 41-76, (1987)
[9] Hadjadj, A.; Kudryavtsev, A., Computation and flow visualization in high-speed aerodynamics, J Turb, 6, 16, (2005)
[10] Hirt, C. W.; Amsden, A.; Cook, J. L., An arbitrary Lagrangian-Eulerian computing method for all flow speeds, J Comput Phys, 14, 227-253, (1974) · Zbl 0292.76018
[11] Glimm, J.; Grove, J. W.; Li, X. L.; Oh, W.; Sharp, D. H., A critical analysis of Rayleigh-Taylor growth rates, J Comput Phys, 169, 652-677, (2001) · Zbl 1011.76057
[12] Glimm, J.; Grove, J. W.; Li, X. L.; Shyue, K. M.; Zhang, Q.; Zeng, Y., Three dimensional front tracking, SIAM J Sci Comput, 19, 703-727, (1998) · Zbl 0912.65075
[13] Kucharik, M.; Garimella, R. V.; Schofield, S. P.; Shashkov, M. J., A comparative study of interface reconstruction methods for multi-material ALE simulations, J Comput Phys, 229, 7, 2432-2452, (2010) · Zbl 1423.76343
[14] 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
[15] Loubère, R.; Maire, P.-H.; Shashkov, M., Reale: a reconnection arbitrary-Lagrangian-Eulerian method in cylindrical geometry, Comput Fluids, 46, 59-69, (2011) · Zbl 1305.76066
[16] Maire, P.-H., A high-order cell-centered Lagrangian scheme for two-dimensional compressible fluid flows on unstructured meshes, J Comput Phys, 228, 7, 2391-2425, (2009) · Zbl 1156.76434
[17] Maire, P.-H.; Abgrall, R.; Breil, J.; Ovadia, J., A cell-centered Lagrangian scheme for two-dimensional compressible flow problems, SIAM J Sci Comput, 29, 4, 1781-1824, (2007) · Zbl 1251.76028
[18] Maire P-H. Contribution to the numerical modeling of Inertial Confinement Fusion, Habilitation à Diriger des Recherches, Bordeaux University; 2011. <http://tel.archives-ouvertes.fr/docs/00/58/97/58/PDF/hdrmain.pdf>.
[19] Shashkov, M., Closure models for multidimensional cells in arbitrary Lagrangian-Eulerian hydrocodes, Int J Numer Methods Fluids, 56, 1497-1504, (2008) · Zbl 1151.76026
[20] Rider, W. J.; Kothe, D., Reconstructing volume tracking, J Comput Phys, 141, 112-152, (1998) · Zbl 0933.76069
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.