Large eddy simulation of turbulent Taylor-Couette flow using isogeometric analysis and the residual-based variational multiscale method

Journal of Computational Physics

Volumn 229, Issue 9, 2010, Pages 3402-3414

  Bazilevs, Y ^a   Akkerman, I ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Boundary layers; Finite elements; Fluids; Isogeometric analysis; Large eddy simulation; Navier Stokes equations; NURBS; Rotating flows; Taylor Couette flow; Turbulence; Weak boundary conditions

Indexed keywords

BOUNDARY CONDITIONS; BOUNDARY LAYERS; FINITE ELEMENT METHOD; NAVIER STOKES EQUATIONS; REYNOLDS NUMBER; TURBULENCE; TURBULENT FLOW;

FINITE ELEMENT; ISOGEOMETRIC ANALYSIS; LARGE-EDDY SIMULATIONS; MULTI-SCALE TURBULENCE; NAVIER-STOKES EQUATION; NURBS; ROTATING FLOW; TAYLOR COUETTE FLOW; VARIATIONAL MULTISCALE; WEAK BOUNDARY CONDITIONS;

LARGE EDDY SIMULATION;

EID: 77949323131     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2010.01.008     Document Type: Article

References (51)

1. Akkerman I., Bazilevs Y., Calo V.M., Hughes T.J.R., Hulshoff S. The role of continuity in residual-based variational multiscale modeling of turbulence. Computational Mechanics 2008, 41:371-378.
2. Arnold D.N., Brezzi F., Cockburn B., Marini L.D. Unified analysis of discontinuous Galerkin methods for elliptic problems. SIAM Journal of Numerical Analysis 2002, 39:1749-1779.
3. Bazilevs Y., Calo V.M., Cottrel J.A., Hughes T.J.R., Reali A., Scovazzi G. Variational multiscale residual-based turbulence modeling for large eddy simulation of incompressible flows. Computer Methods in Applied Mechanics and Engineering 2007, 197:173-201.
4. Bazilevs Y., Calo V.M., Hughes T.J.R., Zhang Y. Isogeometric fluid-structure interaction: theory, algorithms, and computations. Computational Mechanics 2008, 43:3-37.
5. Bazilevs Y., Beirao da Veiga L., Cottrell J.A., Hughes T.J.R., Sangalli G. Isogeometric analysis: approximation stability, and error estimates for h-refined meshes. Mathematical Models and Methods in Applied Sciences 2006, 16:1031-1090.
6. Bazilevs Y., Hughes T.J.R. Weak imposition of Dirichlet boundary conditions in fluid mechanics. Computers and Fluids 2007, 36:12-26.
7. Bazilevs Y., Hughes T.J.R. NURBS-based isogeometric analysis for the computation of flows about rotating components. Computational Mechanics 2008, 43:143-150.
8. Bazilevs Y., Michler C., Calo V.M., Hughes T.J.R. Weak Dirichlet boundary conditions for wall-bounded turbulent flows. Computer Methods in Applied Mechanics and Engineering 2007, 196:4853-4862.
9. Bazilevs Y., Michler C., Calo V.M., Hughes T.J.R. Isogeometric variational multiscale modeling of wall-bounded turbulent flows with weakly-enforced boundary conditions on unstretched meshes. Computer Methods in Applied Mechanics and Engineering 2010, 199:780-790.
10. Bilson M., Bremhorst K. Direct numerical simulation of turbulent Taylor-Couette flow. Journal of Fluid Mechanics 2007, 579:227-270.
11. Brooks A.N., Hughes T.J.R. Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations. Computer Methods in Applied Mechanics and Engineering 1982, 32:199-259.
12. 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.
13. Chung J., Hulbert G.M. A time integration algorithm for structural dynamics with improved numerical dissipation: the generalized-α method. Journal of Applied Mechanics 1993, 60:371-375.
14. Cottrell J.A., Hughes T.J.R., Bazilevs Y. Isogeometric Analysis: Toward Integration of CAD and FEA 2009, Wiley, Chichester.
15. Dong S. DNS of turbulent Taylor-Couette flow. Journal of Fluid Mechanics 2007, 587:373-393.
16. Dong S. Turbulent flow between counter-rotating concentric cylinders: a DNS study. Journal of Fluid Mechanics 2008, 615:371-399.
17. Evans J.A., Bazilevs Y., Babuška I., Hughes T.J.R. N-widths sup-infs and optimality ratios for the k-version of the isogeometric finite element method. Computer Methods in Applied Mechanics and Engineering 2009, 198:1726-1741.
18. Farin G.E. NURBS Curves and Surfaces: From Projective Geometry to Practical Use 1995, A.K. Peters, Ltd., Natick, MA.
19. Franca L.P., Frey S. Stabilized finite element methods: II. The incompressible Navier-Stokes equations. Computer Methods in Applied Mechanics and Engineering 1992, 99:209-233.
20. Gomez H., Calo V.M., Bazilevs Y., Hughes T.J.R. Isogeometric analysis of the Cahn-Hilliard phase-field model. Computer Methods in Applied Mechanics and Engineering 2008, 197:4333-4352.
21. Holmen J., Hughes T.J.R., Oberai A.A., Wells G.N. Sensitivity of the scale partition for variational multiscale LES of channel flow. Physics of Fluids 2004, 16:824-827.
22. Hughes T.J.R. Multiscale phenomena: Green's functions, the Dirichlet-to-Neumann formulation subgrid scale models, bubbles and the origins of stabilized methods. Computer Methods in Applied Mechanics and Engineering 1995, 127:387-401.
23. Hughes T.J.R., Feijóo G., Mazzei L., Quincy J.B. The variational multiscale method - a paradigm for computational mechanics. Computer Methods in Applied Mechanics and Engineering 1998, 166:3-24.
24. Hughes T.J.R., Calo V.M., Scovazzi G. Variational and multiscale methods in turbulence. Proceedings of the XXI International Congress of Theoretical and Applied Mechanics (IUTAM) 2004, Kluwer. W. Gutkowski, T.A. Kowalewski (Eds.).
25. Hughes T.J.R., Cottrell J.A., Bazilevs Y. Isogeometric analysis: CAD, finite elements, NURBS, exact geometry, and mesh refinement. Computer Methods in Applied Mechanics and Engineering 2005, 194:4135-4195.
26. Hughes T.J.R., Mazzei L., Jansen K.E. Large-eddy simulation and the variational multiscale method. Computing and Visualization in Science 2000, 3:47-59.
27. Hughes T.J.R., Mazzei L., Oberai A.A., Wray A.A. The multiscale formulation of large eddy simulation: decay of homogenous isotropic turbulence. Physics of Fluids 2001, 13:505-512.
28. Hughes T.J.R., Oberai A.A., Mazzei L. Large-eddy simulation of turbulent channel flows by the variational multiscale method. Physics of Fluids 2001, 13:1784-1799.
29. Hughes T.J.R., Sangalli G. Variational multiscale analysis: the fine-scale Green's function, projection, optimization, localization, and stabilized methods. SIAM Journal of Numerical Analysis 2007, 45:539-557.
30. Hughes T.J.R., Scovazzi G., Franca L.P. Multiscale and stabilized methods. Computational Fluid Dynamics 2004, vol. 3. Wiley, Chapter 2. E. Stein, R. de Borst, T.J.R. Hughes (Eds.).
31. R Hughes T.J., Tezduyar T.E. Finite element methods for first-order hyperbolic systems with particular emphasis on the compressible Euler equations. Computer Methods in Applied Mechanics and Engineering 1984, 45:217-284.
32. Hughes T.J.R., Wells G.N., 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. Physics of Fluids 2004, 16:4044-4052.
33. Jansen K.E., Whiting C.H., Hulbert G.M. A generalized-α method for integrating the filtered Navier-Stokes equations with a stabilized finite element method. Computer Methods in Applied Mechanics and Engineering 1999, 190:305-319.
34. Johnson C. Numerical Solution of Partial Differential Equations by the Finite Element Method 1987, Cambridge University Press, Sweden.
35. Kirby R.M., Karniadakis G.E. Spectral element and hp methods. Computational Fluid Dynamics 2004, vol. 3. Wiley. E. Stein, R. de Borst, T.J.R. Hughes (Eds.).
36. Kravchenko A.G., Moin P., Moser R. Zonal embedded grids for numerical simulation of wall-bounded turbulent flows. Journal of Computational Physics 1996, 127:412-423.
37. Kravchenko A.G., Moin P., Shariff K. B-spline method and zonal grids for simulation of complex turbulent flows. Journal of Computational Physics 1999, 151:757-789.
38. Kwok W.Y., Moser R.D., Jiménez J. A critical evaluation of the resolution properties of B-spline and compact finite difference methods. Journal of Computational Physics 2001, 174:510-551.
39. Lewis G., Swinney H. Velocity structure functions, scaling and transitions in high-Reynolds-number Couette-Taylor flow. Phys. Rev. E 1999, 59:5457-5467.
40. Moser R.D., Moin P., Leonard A. A spectral numerical method for the Navier-Stokes equations with applications to Taylor-Couette flow. Journal of Computational Physics 1983, 52:524-544.
41. Nitsche J. Uber ein variationsprinzip zur losung von Dirichlet-problemen bei verwendung von teilraumen, die keinen randbedingungen unterworfen sind. Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg 1971, 36:9-15.
42. Orlandi P., Ebstein D. Turbulent budgets in rotating pipes by DNS. International Journal of Heat and Fluid Flow 2000, 21:499-505.
43. Piegl L., Tiller W. The NURBS Book. Monographs in Visual Communication 1997, Springer-Verlag, New York. second ed.
44. Pirro D., Quadrio M. Direct numerical simulation of turbulent Taylor-Couette flow. European Journal of Mechanics - B/Fluids 2007, 27:552-566.
45. Shariff K., Moser R.D. Two-dimensional mesh embedding for B-spline methods. Journal of Computational Physics 1998, 145:471-488.
46. Spalding D.B. A single formula for the law of the wall. Journal of Applied Mechanics 1961, 28:444-458.
47. Speziale C.G., Younis B.A., Rubinstein R., Zhou Y. On consistency conditions for rotating turbulent flows. Physics of Fluids 1998, 10:2108-2110.
48. Tezduyar T., Aliabadi S., Behr M., Johnson A., Mittal S. Parallel finite element computation of 3D flows. Computer 1993, 26:27-36.
49. Tezduyar T.E. Computation of moving boundaries and interfaces and stabilization parameters. International Journal of Numerical Methods in Fluids 2003, 43:555-575.
50. Tezduyar T.E., Aliabadi S.K., Behr M., Mittal S. Massively parallel finite element simulation of compressible and incompressible flows. Computer Methods in Applied Mechanics and Engineering 1994, 119:157-177.
51. Vastano J.A., Moser R.D. Short-time Lyapunov exponent analysis and the transition to chaos in Taylor-Couette flow. Journal of Fluid Mechanics 1991, 233:83-118.