An algebraic variational multiscale-multigrid method for large eddy simulation of turbulent flow

Computer Methods in Applied Mechanics and Engineering

Volumn 199, Issue 13-16, 2010, Pages 853-864

  Gravemeier, Volker ^a   Gee, Michael W ^a   Kronbichler, Martin ^b   Wall, Wolfgang A ^a  

^a TECHNICAL UNIVERSITY OF MUNICH   (Germany)

^b UPPSALA UNIVERSITY   (Sweden)

Author keywords

Algebraic multigrid; Large eddy simulation; Scale separation; Turbulent flow; Variational multiscale method

Indexed keywords

ALGEBRAIC MULTIGRID; ALGEBRAIC MULTIGRID METHODS; ALGEBRAIC MULTIGRIDS; DISCRETIZATIONS; EFFICIENT IMPLEMENTATION; GEOMETRIC MULTIGRID METHODS; HIGHLY SENSITIVE; LID-DRIVEN CAVITIES; MULTIGRID METHODS; RECIRCULATING FLOW; REYNOLDS STRESS TENSORS; ROOT MEAN SQUARES; SCALE SEPARATION; STATE-OF-THE-ART METHODS; TRANSFER OPERATOR; VARIATIONAL MULTISCALE; VARIATIONAL MULTISCALE METHODS;

ATMOSPHERIC BOUNDARY LAYER; DIRECT NUMERICAL SIMULATION; LARGE EDDY SIMULATION; NUMERICAL METHODS; SEPARATION; TURBULENT FLOW;

ALGEBRA;

EID: 74049120805     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2009.05.017     Document Type: Article

References (58)

1. Moin P., and Mahesh K. Direct numerical simulation: a tool in turbulence research. Ann. Rev. Fluid Mech. 30 (1998) 539-578
2. Sagaut P. Large Eddy Simulation for Incompressible Flows. 3rd ed. (2006), Springer-Verlag, Berlin
3. Kolmogorov A.N. The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers (in Russian). Dokl. Akad. Nauk. SSSR 30 (1941) 299-303
4. Hughes T.J.R., Mazzei L., and Jansen K.E. Large eddy simulation and the variational multiscale method. Comput. Visual. Sci. 3 (2000) 47-59
5. Collis S.S. Monitoring unresolved scales in multiscale turbulence modeling. Phys. Fluids 13 (2001) 1800-1806
6. Gravemeier V., Wall W.A., and Ramm E. A three-level finite element method for the instationary incompressible Navier-Stokes equations. Comput. Meth. Appl. Mech. Engrg. 193 (2004) 1323-1366
7. Gravemeier V. The variational multiscale method for laminar and turbulent flow. Arch. Comput. Meth. Engng. 13 (2006) 249-324
8. John V. On large eddy simulation and variational multiscale methods in the numerical simulation of turbulent incompressible flows. Appl. Math. 4 (2006) 321-353
9. Hackbusch W. Multigrid methods and applications. Computational Mathematics vol. 4 (1985), Springer-Verlag, Berlin
10. Briggs W.L., Henson V.E., and McCormick S.F. A multigrid tutorial. 2nd ed. (2000), SIAM, Philadelphia, PA
11. Trottenberg U., Oosterlee C., and Schüller A. Multigrid (2001), Elsevier Academic Press, London
12. Gravemeier V. Scale-separating operators for variational multiscale large eddy simulation of turbulent flows. J. Comput. Phys. 212 (2006) 400-435
13. Lallemand M.-H., Steve H., and Dervieux A. Unstructured multigridding by volume agglomeration: current status. Comput. Fluids 21 (1992) 397-433
14. Koobus B., and Farhat C. A variational multiscale method for the large eddy simulation of compressible turbulent flows on unstructured meshes-application to vortex shedding. Comput. Meth. Appl. Mech. Engrg. 193 (2004) 1367-1383
15. P. Voke, Multiple mesh simulation of low Reynolds number turbulent channel flow, in: C. Taylor, R. Sani (Eds.), Numerical Methods in Laminar and Turbulent Flow, vol. 6, 1989, pp. 1567-1577.
16. Terracol M., Sagaut P., and Basdevant C. A multilevel algorithm for large-eddy simulation of turbulent compressible flows. J. Comput. Phys. 167 (2001) 439-474
17. Sagaut P., Deck S., and Terracol M. Multiscale and Multiresolution Approaches in Turbulence (2006), Imperial College Press, London
18. Ruge J., and Stüben K. Algebraic multigrid (AMG). In: McCormick S.F. (Ed). Multigrid Methods. Frontiers in Applied Mathematics vol. 3 (1987), SIAM, Philadelphia, PA 73-130
19. Vaněk P., Mandel J., and Brezina M. Algebraic multigrid based on smoothed aggregation for second and fourth order problems. Computing 56 (1996) 179-196
20. Y. Notay, Algebraic analysis of two-grid methods: the nonsymmetric case, Num. Lin. Alg. Appl., in press. Available from: .
21. P. Vaněk, A. Janka, H. Guillard, Convergence of Algebraic Multigrid Based on Smoothed Aggregation II: Extension to a Petrov-Galerkin Method, Technical Report 3683, INRIA, 1999.
22. Sala M., and Tuminaro R.S. A new Petrov-Galerkin smoothed aggregation preconditioner for nonsymmetric linear systems. SIAM J. Sci. Comp. 31 (2008) 143-166
23. Lin P.T., Sala M., Shadid J.N., and Tuminaro R.S. Performance of fully coupled algebraic multilevel domain decomposition preconditioners for incompressible flow and transport. Int. J. Numer. Meth. Engrg. 67 (2006) 208-225
24. Mavriplis D.J., and Venkatakrishnan V. A 3D agglomeration multigrid solver for the Reynolds-averaged Navier-Stokes equations on unstructured meshes. Int. J. Numer. Meth. Fluids 23 (1996) 527-544
25. Carre G., and Lanteri S. Parallel linear multigrid by agglomeration for the acceleration of 3D compressible flow calculations on unstructured meshes. Num. Alg. 24 (2000) 309-322
26. Bazilevs Y., Calo V.M., Cottrell J.A., Hughes T.J.R., Reali A., and Scovazzi G. Variational multiscale residual-based turbulence modeling for large eddy simulation of incompressible flows. Comput. Meth. Appl. Mech. Engrg. 197 (2007) 173-201
27. Hughes T.J.R., Scovazzi G., and Franca L.P. Multiscale and stabilized methods. In: Stein E., de Borst R., and Hughes T.J.R. (Eds). Encyclopedia of Computational Mechanics (2004), John Wiley & Sons, Chichester
28. Codina R., Principe J., Guasch O., and Badia S. Time dependent subscales in the stabilized finite element approximation of incompressible flow problems. Comput. Meth. Appl. Mech. Engrg. 196 (2007) 2413-2430
29. P. Gamnitzer, V. Gravemeier, W.A. Wall, Time-dependent subgrid scales in residual-based large eddy simulation of turbulent channel flow, Comput. Meth. Appl. Mech. Engrg. (submitted for publication).
30. Harten A. Multiresolution representation of data: a general framework. SIAM J. Numer. Anal. 33 (1996) 1205-1256
31. Smagorinsky J. General circulation experiments with the primitive equations. I. The basic experiment. Mon. Weather Rev. 91 (1963) 99-164
32. Pope S.B. Turbulent Flows (2000), Cambridge University Press, Cambridge
33. Brezzi F., and Fortin M. Mixed and Hybrid Finite Element Methods (1991), Springer-Verlag, New York
34. Hughes T.J.R., Franca L.P., and Balestra M. A new finite element formulation for computational fluid dynamics: V. Circumventing the Babuska-Brezzi condition: a stable Petrov-Galerkin formulation of the Stokes problem accommodating equal-order interpolation. Comput. Meth. Appl. Mech. Engrg. 59 (1986) 85-99
35. Tezduyar T.E., Mittal S., Ray S.E., and Shih R. Incompressible flow computations with stabilized bilinear and linear equal-order-interpolation velocity-pressure elements. Comput. Meth. Appl. Mech. Engrg. 95 (1992) 221-242
36. Franca L.P., and Valentin F. On an improved unusual stabilized finite element method for the advective-reactive-diffusive equation. Comput. Meth. Appl. Mech. Engrg. 190 (2000) 1785-1800
37. Barrenechea G., and Valentin F. An unusual stabilized finite element method for a generalized Stokes problem. Numer. Math. 92 (2002) 652-677
38. Harari I., and Hughes T.J.R. What are c and h?: inequalities for the analysis and design of finite element methods. Comput. Meth. Appl. Mech. Engrg. 97 (1992) 157-192
39. Moulton J.D., Dendy Jr. J.E., and Hyman J.M. The black box multigrid numerical homogenization algorithm. J. Comp. Phys. 142 (1998) 80-108
40. Knapek S. Matrix-dependent multigrid homogenization for diffusion problems. SIAM J. Sci. Comp. 20 (1998) 515-533
41. M. Brezina, T. Manteuffel, S. McCormick, J. Ruge, G. Sanders, Towards adaptive smoothed aggregation (αSA) for nonsymmetric problems, SIAM J. Sci. Comp. (submitted for publication).
42. R. Tuminaro, C. Tong, Parallel smoothed aggregation multigrid: aggregation strategies on massively parallel machines, in: J. Donnelley (Ed.), Super Computing 2000 Proceedings, 2000.
43. Vaněk P., Brezina M., and Mandel J. Convergence of algebraic multigrid based on smoothed aggregation. Numer. Math. 88 (2001) 559-579
44. M.W. Gee, C.M. Siefert, J.J. Hu, R.S. Tuminaro, M.G. Sala, ML 5.0 Smoothed Aggregation User's Guide, Technical Report SAND2006-2256, Sandia National Laboratories, 2006.
45. V. Gravemeier, M.W. Gee, W.A. Wall, An algebraic variational multiscale-multigrid method based on plain aggregation for convection-diffusion problems, Comput. Meth. Appl. Mech. Engrg. (submitted for publication).
46. John V., and Kaya S. A finite element variational multiscale method for the Navier-Stokes equations. SIAM J. Sci. Comp. 26 (2005) 1485-1503
47. Deardorff J.W. A numerical study of three-dimensional turbulent channel flow at large Reynolds numbers. J. Fluid Mech. 41 (1970) 453-465
48. Germano M., Piomelli U., Moin P., and Cabot W.H. A dynamic subgrid-scale eddy viscosity model. Phys. Fluids A 3 (1991) 1760-1765
49. Lilly D.K. A proposed modification of the Germano subgrid-scale closure method. Phys. Fluids A 4 (1992) 633-635
50. τ = 590. Phys. Fluids 11 (1999) 943-945
51. Jansen K.E., Whiting C.H., and Hulbert G.M. A generalized-α method for integrating the filtered Navier-Stokes equations with a stabilized finite element method. Comput. Meth. Appl. Mech. Engrg. 190 (2000) 305-319
52. Prasad A.K., and Koseff J.R. Reynolds number and end-wall effects on a lid-driven cavity flow. Phys. Fluids A 1 (1989) 208-218
53. Zang Y., Street R.L., and Koseff J.R. A dynamic mixed subgrid-scale model and its application to turbulent recirculating flows. Phys. Fluids A 5 (1993) 3186-3196
54. Bouffanais R., Deville M.O., and Leriche E. Large-eddy simulation of the flow in a lid-driven cubical cavity. Phys. Fluids 19 (2007) 055108-1-055108-20
55. Deshpande M.D., and George Milton S. Kolmogorov scales in a driven cavity flow. Fluid Dyn. Res. 22 (1998) 359-381
56. Leriche E., and Gavrilakis S. Direct numerical simulation of the flow in a lid-driven cubical cavity. Phys. Fluids 12 (2000) 1363-1376
57. Shankar P.N., and Deshpande M.D. Fluid mechanics in the driven cavity. Ann. Rev. Fluid Mech. 32 (2000) 93-136
58. V. Gravemeier, M. Kronbichler, M.W. Gee, W.A. Wall, Fourier analysis of an algebraic variational multiscale-multigrid method for large eddy simulation and application to turbulent flow past a square-section cylinder (in preparation).