×

zbMATH — the first resource for mathematics

Unstructured multigridding by volume agglomeration: Current status. (English) Zbl 0753.76136
Summary: We describe a multigrid (MG) method for solving the Euler equations as applied to non-structured meshes in two (triangles) and three dimensions (tetrahedra). The main idea is to coarsen the given mesh by using topological neighboring relations. It is applied to upwind solvers relying on the MUSCL methodology. Two MG schemes are presented: an explicit Runge-Kutta FAS, and an implicit correction scheme. Transonic external flow computations are described for illustration.

MSC:
76M25 Other numerical methods (fluid mechanics) (MSC2010)
76N15 Gas dynamics (general theory)
65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Angrand, F.; Leyland, P., Schéma multigrille dynamique pour la simulation d’écoulements de fluides visqueux compressibles, INRIA research report 659, (1987)
[2] Bank, R.; Sherman, A., A multi-level iterative method for solving finite-element equations, (), 117-126
[3] Perez, E.; Périaux, J.; Rosenblum, J.-P.; Stoufflet, B.; Dervieux, A.; Lallemand, M.-H., Adaptive full-multigrid finite element methods for solving the two-dimensional Euler equations, (), 523-527
[4] Perez, E., Finite element and multigrid solution of the two-dimensional Euler equations on a non-structured mesh, INRIA research report 442, (1985)
[5] Lallemand, M.-H.; Fezoui, L.; Perez, E., Un schéma multigrille en éléments finis décentrés pour LES equations d’Euler, INRIA research report 602, (1987)
[6] Leclercq, M.-P., Résolution des équations d’Euler par des méthodes multigrilles; conditions aux limites en régime hypersonique, Thesis, (1990), St-Etienne
[7] Loehner, R.; Morgan, K., Unstructured multigrid methods, () · Zbl 0624.65102
[8] Mavriplis, D.; Jameson, A., A multi-grid solution of the two-dimensional Euler equations on unstructured tirangular meshes, AIAA paper 87-0353, (1987)
[9] Brandt, A.; McCormick, S.F.; Ruge, J., Algebraic multigrid (AMG) for sparse matrix equations, (), 257-284 · Zbl 0548.65014
[10] Ruge, J.; Stueben, K., Efficient solution of finite difference and finite element equations, (), 169-212
[11] Fezoui, L., Résolution des équations d’Euler par un schéma de Van leer en éléments finis, INRIA research report 358, (1985)
[12] Fezoui, L.; Stoufflet, B., A class of implicit upwind schemes for Euler simulations with unstructured meshes, J. comput. phys., 84, 174, (1989) · Zbl 0677.76062
[13] Zienkiewicz, O.C., The finite element in engineering science, (1971), McGraw-Hill London · Zbl 0237.73071
[14] Osher, S.; Solomon, F., Upwind difference schemes for hyperbolic systems of conservation laws, Maths comput., 38, 339, (1982) · Zbl 0483.65055
[15] Stoufflet, B.; Périaux, J.; Fezoui, L.; Dervieux, A., Numerical simulation of 3-D hypersonic Euler flows around space vehicles, AIAA paper 87-0560, (1987)
[16] van Leer, B., Flux vector splitting for the Euler equations, (), 405-512
[17] van Leer, B., Computational methods for ideal compressible flow, () · Zbl 1114.76049
[18] Jameson, A., Numerical solution of the Euler equations for compressible inviscid fluids, (), 199-245
[19] Turkel, E.; van Leer, B., Flux vector splitting and Runge-Kutta methods for the Euler equations, ICASE report 84-27, (1984)
[20] Lallemand, M.-H., Schémas décentrés multigrilles pour la résolution des équations d’Euler en éléments finis, ()
[21] Benkhaldoun, F.; Dervieux, A.; Fernandez, G.; Guillard, H.; Larrouturou, B., Some investigations of finite-element solutions to stiff combustion problems: mesh adaption and implicit time-stepping, (), 393-410
[22] Steger, J.; Warming, R.F., Flux vector splitting for the inviscid gas dynamic with applications to finite-difference methods, J. comput. phys., 40, 263, (1981) · Zbl 0468.76066
[23] Steve, H., Schémas implicites linearisés décentrés pour la résolution des équations d’Euler en plusieurs dimensions, ()
[24] Desideri, J.-A., Preliminary results on iterative convergence of a class of implicit schemes, INRIA research report 490, (1986)
[25] Boehmer, K.; Hemker, P.; Stetter, H.J., The defect correction approach, Comput. suppl., 5, 1, (1984) · Zbl 0551.65034
[26] Hemker, P.; Spekreijse, S., Multiple grid and Osher’s scheme for the efficient solution of the steady Euler equations, Appl. numer. math., 2, 475, (1986) · Zbl 0612.76077
[27] Koren, B.; Lallemand, M.-H., Iterative defect correction and multigrid accelerated explicit time stepping schemes for the steady Euler equations, CWI report NM-R8908, (1989)
[28] Anderson, W.K.; Thomas, J.-L.; Whitefield, D.L., Multigrid acceleration of the flux split Euler equations, AIAA paper 86-0274, (1986)
[29] Mulder, W.A., Multigrid relaxation for the Euler equation, J. comput. phys., 77, 183, (1988)
[30] Haenel, D.; Meinke, M.; Schroeder, W., Application of the multigrid method in solutions of the compressible Navier-Stokes equations, (), 234-254
[31] Fernandez, G.; Guillard, H., Implicit schemes for combustion problems, (), 277-286
[32] Koren, B., Robustness improvement of point Gauss-Seidel relaxation for steady, hypersonic flow computations, Cwinm-n8805, (1988), Amsterdam
[33] ()
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.