Preconditioned spectral multi-domain discretization of the incompressible Navier-Stokes equations

Journal of Computational Physics

Volumn 201, Issue 1, 2004, Pages 204-223

  Manna, Marcello ^a   Vacca, Andrea ^b   Deville, Michel O ^c  

^a UNIVERSITY OF NAPLES FEDERICO II   (Italy)

^b SECOND UNIVERSITY OF NAPLES   (Italy)

^c EPFL   (Switzerland)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL FLUID DYNAMICS; ITERATIVE METHODS; NAVIER STOKES EQUATIONS; NUMBER THEORY; VISCOUS FLOW;

DOMAIN DISCRETIZATION; INCOMPRESSIBLE (NAVIER )STOKES EQUATION; INCOMPRESSIBLE NAVIER STOKES EQUATIONS; ITERATIVE SOLUTIONS; MULTI-DOMAINS; NUMERICAL SOLUTION; SCHUR COMPLEMENT MATRIX; SPECTRAL COLLOCATION; SUBDOMAIN; THREE SPACE DIMENSIONS;

LARGE EDDY SIMULATION;

EID: 13844262833     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jcp.2004.05.011     Document Type: Article

References (41)

1. Kim J. Moin P. Moser R. Turbulence statistics in fully developed channel flow at low Reynolds number J. Fluid Mech 177 1987 133-166
2. θ = 1410 J. Fluid Mech 187 1988 61-97
3. Rai M. Moin P. Direct numerical simulation of transition and turbulence in a spatially evolving boundary layer J. Comput. Phys 109 1993 169-192
4. Moser R. Kim J. Mansour N. Direct numerical simulation of turbulent channel flow up Re = 590 Phys. Fluids 11 4 1999 1938-1944
5. Wu X. Jacobs R. Hunt J. Durbin P. Simulation of boundary layer transition induced by periodically passing wakes J. Fluid Mech 398 1999 109-153
6. Jiménez J. Moser R.D. Large-eddy simulations where are we and what can we expect? AIAA J 38 2000 605-612
7. Sagaut P. Large Eddy Simulation for Incompressible Flows. An Introduction 2001 Springer Berlin
8. Wallace J.M. Eckelmann H. Brodkey R.S. The wall region in turbulent shear flow J. Fluid Mech 54 1972 39-48
9. Smith B. Bjorstad P. Gropp W. Domain Decomposition 2000 Cambridge University Press New York
10. Quarteroni A. Valli A. Domain Decomposition Methods for Partial Differential Equations 2000 Oxford University Press Oxford
11. Patera A.T. A spectral element method for fluid dynamics: Laminar flow in a channel expansion J. Comput. Phys 54 1984 468-488
12. Maday Y. Patera A.T. Spectral element methods for the Navier-Stokes equations in: Noor A.K. Oden J.T. (Eds.), State-of-the-Art Surveys in Computational Mechanics 1989 71-143 ASME New York
13. Henderson R. Karniadakis G. Unstructured spectral element methods for simulation of turbulent flows J. Comput. Phys 122 1995 191-217
14. H.M. Tufo, P.F. Fisher, Tera-scale spectral element algorithms and implementations, in: Proceedings of the ACM/IEEE SC99 Conference on High Performance Networking and Computing, IEEE Computer Society, 1999, pages CD-Rom
15. Tufo H.M. Fisher P.F. Fast parallel direct solvers for coarse-grid problems J. Parallel Distrib. Comput 61 2001 151-177
16. Rønquist E.M. A domain decomposition method for elliptic boundary value problems: Application to unsteady incompressible fluid flow in: Keyes D.E. Chan T.F. Meurant G. Scroggs J.S. Voigt R.G. (Eds.), Proceedings of the Fifth Conference on Domain Decomposition Methods for Partial Differential Equations 1992 545-557 SIAM Philadelphia
17. Rønquist E.M. A domain decomposition solver for three-dimensional steady free surface flows flows in: Espedal M. Bjorstad P. Keyes D.E. (Eds.), Domain Decomposition 9 Proceedings 1998 792-801 Wiley New York
18. Orszag S.A. Spectral methods for problems in complex geometries J. Comput. Phys 37 1980 70-92
19. Gervasio P. Ovtchinnikov E. Quarteroni A. The spectral projection decomposition method for elliptic equations in two dimensions SIAM J. Numer. Anal 4 1997 1616-1639
20. Pinelli A. Vacca A. Quarteroni A. A spectral multidomain method for the numerical simulation of turbulent flows J. Comput. Phys 136 1997 546-558
21. Bernardi C. Maday Y. Patera A.T. in: Brezis H. Lions J.L. (Eds.), A New Non-conforming Approach to Domain Decomposition: The Mortar Element Method vol. XI 1994 13-51 Pitman Boston
22. Arnold D.N. Brezzi F. Cockburn B. Marini L.D. Unified analysis of discontinuous Galerkin methods for elliptic problems SIAM J. Numer. Anal 39 2002 1749-1779
23. Couzy W. Deville M. A fast Schur complement method for the spectral element discretization of the incompressible Navier-Stokes equations J. Comput. Phys 116 1995 135-142
24. Deville M.O. Fisher P.F. Mund E.H. High-order Methods for Incompressible Fluid Flow 2002 Cambridge University Press New York
25. Pavarino L.F. Widlund O.B. A polylogarithmic bound for an iterative substructuring method for spectral elements in three dimensions SIAM J. Numer. Anal 33 1996 1303-1335
26. Casarin M.A. Quasi-optimal Schwarz methods for the conforming spectral element discretization SIAM J. Numer. Anal 34 1997 2482-2502
27. Pavarino L.F. Warburton T. Overlapping Schwarz methods for unstructured spectral elements J. Comput. Phys 160 2000 298-317
28. Van Kan J. A second order accurate pressure correction scheme for viscous incompressible flow SIAM J. Sci. Stat. Comput 7 1986 870-891
29. Shen J. On error estimates of the projection methods for the Navier-Stokes equations: Second order schemes Math. Comput 65 215 1996 1039-1065
30. Canuto C. Hussaini M.Y. Quarteroni A. Zang T.A. Spectral Methods In Fluid Dynamics 1988 Springer New York
31. Golub G. Van Loan C. Matrix Computations 1989 The John Hopkins University Press Baltimore, MD
32. Bernardi C. Maday Y. Approximations Spectrales de Problèmes aux Limites Elliptiques 1992 Springer Paris
33. Chan T.F. Goovaerts D. Schur complement domain decomposition algorithms for spectral methods Appl. Numer. Math 6 1989 53-64
34. Chan T.F. Mathew T.P. Shao J.P. Efficient variants of the vertex space domain decomposition algorithm SIAM J. Sci. Stat. Comput 15 6 1994 1349-1374
35. Smith B.F. An optimal domain decomposition preconditioner for the finite element solution of linear elasticity problems SIAM J. Sci. Stat. Comput 13 1 1992 364-378
36. Bramble J.H. Pasciak J.E. Schatz A.H. The construction of preconditioners for elliptic problems by substructuring I Math. Comput 47 175 1986 103-134
37. Carvalho L.M. Giraud L. Le Tallec P. Algebraic two-level preconditioners for the Schur complement method SIAM J. Sci. Comput 22 6 2001 1987-2005
38. Casarin M.A. Diagonal edge preconditioners in p-version and spectral element methods SIAM J. Sci. Comput 18 2 1997 610-620
39. Patera A.T. Fast direct Poisson solvers for high-order finite element discretizations in rectangularly decomposable domains J. Comput. Phys 65 1986 474-480
40. Germano M. Piomelli U. Moin P. Cabot W.H. A dynamic subgrid scale eddy viscosity model Phys. Fluids 3 1991 1760-1767
41. Lilly D.K. A proposed modification of the Germano subgrid-scale closure method Phys. Fluids 4 3 1992 633-635