Weak Dirichlet boundary conditions for wall-bounded turbulent flows

Computer Methods in Applied Mechanics and Engineering

Volumn 196, Issue 49-52, 2007, Pages 4853-4862

  Bazilevs, Y ^a   Michler, C ^a   Calo, V M ^a   Hughes, T J R ^a  

^a UNIVERSITY OF TEXAS AT AUSTIN   (United States)

Author keywords

Boundary layers; Fluids; Isogeometric analysis; Law of the wall; Navier Stokes equations; Turbulence; Weakly imposed boundary conditions

Indexed keywords

BOUNDARY CONDITIONS; BOUNDARY LAYER FLOW; CHANNEL FLOW; COMPUTER SIMULATION; NAVIER STOKES EQUATIONS; REYNOLDS NUMBER; WALL FLOW;

DIRICHLET BOUNDARY CONDITION; ISOGEOMETRIC ANALYSIS;

TURBULENT FLOW;

BOUNDARY CONDITIONS; BOUNDARY LAYER FLOW; CHANNEL FLOW; COMPUTER SIMULATION; NAVIER STOKES EQUATIONS; REYNOLDS NUMBER; TURBULENT FLOW; WALL FLOW;

EID: 34548746927     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2007.06.026     Document Type: Article

References (34)

1. I. Akkerman, Y. Bazilevs, V.M. Calo, T.J.R. Hughes, S. Hulshoff, The role of continuity in residual-based variational multiscale modeling of turbulence, Comput. Mech. (2007) in press, doi:10.1007/s00466-007-0193-7.
2. Arnold D.N., Brezzi F., Cockburn B., and Marini L.D. Unified analysis of discontinuous Galerkin methods for elliptic problems. SIAM J. Numer. Anal. 39 (2002) 1749-1779
3. Barenblatt G.I. Similarity, Self-similarity, and Intermediate Assymptotics (1979), Consultants Bureau, Plenum Press, New York and London
4. Y. Bazilevs, Isogeometric analysis of turbulence and fluid-structure interaction, Ph.D. thesis, ICES, UT Austin, 2006.
5. Bazilevs Y., Calo V.M., Zhang Y., and Hughes T.J.R. Isogeometric fluid-structure interaction analysis with applications to arterial blood flow. Comput. Mech. 38 (2006) 310-322
6. Y. Bazilevs, V.M. Calo, J.A. Cottrell, T.J.R. Hughes, A. Reali, G. Scovazzi, Variational multiscale residual-based turbulence modeling for large eddy simulation of incompressible flows, Comput. Methods Appl. Mech. Engrg. (2007) in press, doi:10.1016/j.cma.2007.07.016.
7. Bazilevs Y., Beirao da Veiga L., Cottrell J.A., Hughes T.J.R., and Sangalli G. Isogeometric analysis: approximation, stability and error estimates for h-refined meshes. Math. Models Methods Appl. Sci. 16 (2006) 1031-1090
8. Bazilevs Y., and Hughes T.J.R. Weak imposition of Dirichlet boundary conditions in fluid mechanics. Comput. Fluids 36 (2007) 12-26
9. Brooks A.N., and Hughes T.J.R. Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations. Comput. Methods Appl. Mech. Engrg. 32 (1982) 199-259
10. V.M. Calo, Residual-based multiscale turbulence modeling: finite volume simulation of bypass transition, Ph.D. thesis, Department of Civil and Environmental Engineering, Stanford University, 2004.
11. Chung J., and Hulbert G.M. A time integration algorithm for structural dynamics with improved numerical dissipation: the generalized-α method. J. Appl. Mech. 60 (1993) 371-375
12. Cottrell J.A., Reali A., Bazilevs Y., and Hughes T.J.R. Isogeometric analysis of structural vibrations. Comput. Methods Appl. Mech. Engrg. 195 (2006) 5257-5297
13. del Alamo J.C., Jimenez J., Zandonade P., and Moser R.D. Scaling of the energy spectra of turbulent channels. J. Fluid Mech. 500 (2004) 135-144
14. Holmen J., Hughes T.J.R., Oberai A.A., and Wells G.N. Sensitivity of the scale partition for variational multiscale LES of channel flow. Phys. Fluids 16 3 (2004) 824-827
15. Hughes T.J.R. The Finite Element Method: Linear Static and Dynamic Finite Element Analysis (2000), Dover Publications, Mineola, NY
16. Hughes T.J.R., and Mallet M. A new finite element formulation for fluid dynamics: III. The generalized streamline operator for multidimensional advective-diffusive systems. Comput. Methods Appl. Mech. Engrg. 58 (1986) 305-328
17. 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
18. Hughes T.J.R., Mazzei L., Oberai A.A., and Wray A.A. The multiscale formulation of large eddy simulation: decay of homogenous isotropic turbulence. Phys. Fluids 13 2 (2001) 505-512
19. Hughes T.J.R., Oberai A.A., and Mazzei L. Large-eddy simulation of turbulent channel flows by the variational multiscale method. Phys. Fluids 13 6 (2001) 1784-1799
20. 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. Computational Fluid Dynamics vol. 3 (2004), Wiley (Chapter 2)
21. Hughes T.J.R., Calo V.M., and Scovazzi G. Variational and multiscale methods in turbulence. In: Gutkowski W., and Kowalewski T.A. (Eds). Proceedings of the XXI International Congress of Theoretical and Applied Mechanics (IUTAM) (2004), Kluwer
22. Hughes T.J.R., Cottrell J.A., and Bazilevs Y. Isogeometric analysis: CAD, finite elements, NURBS, exact geometry, and mesh refinement. Comput. Methods Appl. Mech. Engrg. 194 (2005) 4135-4195
23. Hughes T.J.R., Wells G.N., and Wray A.A. Energy transfers and spectral eddy viscosity of homogeneous isotropic turbulence: comparison of dynamic Smagorinsky and multiscale models over a range of discretizations. Phys. Fluids 16 (2004) 4044-4052
24. 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. Methods Appl. Mech. Engrg. 190 (1999) 305-319
25. Kravchenko A.G., Moin P., and Moser R. Zonal embedded grids for numerical simulation of wall-bounded turbulent flows. J. Comput. Phys. 127 (1996) 412-423
26. Kravchenko A.G., Moin P., and Shariff K. B-spline method and zonal grids for simulation of complex turbulent flows. J. Comput. Phys. 151 (1999) 757-789
27. Kwok W.Y., Moser R.D., and Jiménez J. A critical evaluation of the resolution properties of B-spline and compact finite difference methods. J. Comput. Phys. 174 (2001) 510-551
28. Mohammadi B., and Pironneau O. Analysis of the K-Epsilon Turbulence Model (1994), John Wiley & Sons, Chichester, England
29. Moser R., Kim J., and Mansour R. DNS of turbulent channel flow up to Re = 590. Phys. Fluids 11 (1999) 943-945
30. Shakib F., Hughes T.J.R., and Johan Z. A new finite element formulation for computational fluid dynamics: X. The compressible Euler and Navier-Stokes equations. Comput. Methods Appl. Mech. Engrg. 89 (1991) 141-219
31. Shariff K., and Moser R.D. Two-dimensional mesh embedding for B-spline methods. J. Comput. Phys. 145 (1998) 471-488
32. Spalding D.B. A single formula for the law of the wall. J. Appl. Mech. 28 (1961) 444-458
33. Tezduyar T.E. Computation of moving boundaries and interfaces and stabilization parameters. Int. J. Numer. Methods Fluids 43 (2003) 555-575
34. Wheeler M.F. An elliptic collocation-finite element method with interior penalties. SIAM J. Numer. Anal. 15 (1978) 152-161