The role of continuity in residual-based variational multiscale modeling of turbulence

Computational Mechanics

Volumn 41, Issue 3, 2008, Pages 371-378

  Akkerman, I ^a   Bazilevs, Y ^b   Calo, V M ^b   Hughes, T J R ^b   Hulshoff, S ^a  

^a DELFT UNIVERSITY OF TECHNOLOGY   (Netherlands)

^b UNIVERSITY OF TEXAS AT AUSTIN   (United States)

Author keywords

Boundary layers; Continuity of discretization; Finite elements; Incompressible flows; Isogeometric Analysis; Navier Stokes equations; NURBS; Residual based turbulence modeling; Turbulent channel flows; Variational multiscale formulation

Indexed keywords

BOUNDARY LAYERS; FINITE ELEMENT METHOD; INCOMPRESSIBLE FLOW; NAVIER STOKES EQUATIONS; REYNOLDS NUMBER;

CONTINUITY OF DISCRETIZATION; ISOGEOMETRIC ANALYSIS; TURBULENT CHANNEL FLOWS; VARIATIONAL MULTISCALE FORMULATION;

TURBULENT FLOW;

EID: 36749054591     PISSN: 01787675     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00466-007-0193-7     Document Type: Article

References (43)

1. Akin JE and Tezduyar TE (2004). Calculation of the advective limit of the SUPG stabilization parameter for linear and higher-order elements. Comput Methods Appl Mech Eng 193: 1909-1922
2. Bazilevs Y (2006) Isogeometric analysis of turbulence and fluid-structure interaction. PhD thesis, ICES, UT Austin
3. Bazilevs Y and Hughes TJR (2007). Weak imposition of Dirichlet boundary conditions in fluid mechanics. Comput Fluids 36: 12-26
4. Bazilevs Y, Beirao da Veiga L, Cottrell JA, Hughes TJR and Sangalli G (2006). Isogeometric analysis: approximation, stability and error estimates for h-refined meshes. Math Models Methods Appl Sci 16: 1031-1090
5. Bazilevs Y, Calo VM, Zhang Y and Hughes TJR (2006). Isogeometric fluid-structure interaction analysis with applications to arterial blood flow. Comput Mech 38: 310-322
6. Bazilevs Y, Calo VM, Cottrell JA, Hughes TJR, Reali A, Scovazzi G (2007) Variational multiscale residual-based turbulence modeling for large eddy simulation of incompressible flows. Comput Methods Appl Mech Eng. Available as ICES Report 07-15, UT Austin (submitted)
7. Bazilevs Y, Michler C, Calo VM, Hughes TJR (2007) Weak Dirichlet boundary conditions for wall-bounded turbulent flows. Comput Methods Appl Mech Eng (accepted for publication)
8. Bischoff M and Bletzinger K-U (2004). Improving stability and accuracy of Reissner-Mindlin plate finite elements via algebraic subgrid scale stabilization. Comput Methods Appl Mech Eng 193: 1491-1516
9. Bochev PB, Gunzburger MD and Shadid JN (2004). On inf-sup stabilized finite element methods for transient problems. Comput Methods Appl Mech Eng 193: 1471-1489
10. Brooks AN and Hughes TJR (1982). Streamline upwind/Petrov- Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations. Comput Methods Appl Mech Eng 32: 199-259
11. Burman E and Hansbo P (2004). Edge stabilization for Galerkin approximations of convection-diffusion-reaction problems. Comput Methods Appl Mech Eng 193: 1437-1453
12. Calo VM (2004) Residual-based multiscale turbulence modeling: finite volume simulation of bypass transistion. PhD thesis, Department of Civil and Environmental Engineering, Stanford University
13. Chung J and Hulbert GM (1993). A time integration algorithm for structural dynamics with improved numerical dissipation: the generalized-α method. J Appl Mech 60: 371-375
14. Codina R and Soto O (2004). Approximation of the incompressible Navier-Stokes equations using orthogonal subscale stabilization and pressure segregation on anisotropic finite element meshes. Comput Methods Appl Mech Eng 193: 1403-1419
15. Codina R, Principe J, Guasch O, Badia S (2007) Time dependent subscales in the stabilized finite element approximation of incompressible flow problems. Comput Methods Appl Mech Eng (accepted for publication)
16. Cohen E, Riesenfeld R and Elber G (2001). Geometric modeling with splines. An introduction. A K Peters Ltd, Wellesley
17. Cottrell JA, Reali A, Bazilevs Y and Hughes TJR (2006). Isogeometric analysis of structural vibrations. Comput Methods Appl Mech Eng 195: 5257-5297
18. Coutinho ALGA, Diaz CM, Alvez JLD, Landau L, Loula AFD, Malta SMC, Castro RGS and Garcia ELM (2004). Stabilized methods and post-processing techniques for miscible displacements. Comput Methods Appl Mech Eng 193: 1421-1436
19. Gravemeier V, Wall WA and Ramm E (2004). A three-level finite element method for the instationary incompressible Navier-Stokes equations. Comput Methods Appl Mech Eng 193: 1323- 1366
20. Harari I (2004). Stability of semidiscrete formulations for parabolic problems at small time steps. Comput Methods Appl Mech Eng 193: 1491-1516
21. Hauke G and Valiño L (2004). Computing reactive flows with a field Monte Carlo formulation and multi-scale methods. Comput Methods Appl Mech Eng 193: 1455-1470
22. Hughes TJR and Mallet M (1986). A new finite element formulation for fluid dynamics: III. The generalized streamline operator for multidimensional advective-diffusive systems. Comput Methods Appl Mech Eng 58: 305-328
23. Hughes TJR, Sangalli G (2006) Variational multiscale analysis: the fine-scale Green's function, projection, optimization, localization, and stabilized methods. SIAM J Numer Anal (accepted). Available as ICES Report 05-46, UT Austin
24. Hughes TJR, Calo VM, Scovazzi G (2004) Variational and multiscale methods in turbulence. In: Gutkowski W, Kowalewski TA (eds) Proceedings of the XXI international congress of theoretical and applied mechanics (IUTAM). Kluwer, Dordrecht
25. Hughes TJR, Cottrell JA and Bazilevs Y (2005). Isogeometric analysis: CAD, finite elements, NURBS, exact geometry, and mesh refinement. Comput Methods Appl Mech Eng 194: 4135-4195
26. Jansen KE, Whiting CH and Hulbert GM (1999). A generalized-α method for integrating the filtered Navier-Stokes equations with a stabilized finite element method. Comput Methods Appl Mech Eng 190: 305-319
27. Johnson C (1987). Numerical solution of partial differential equations by the finite element method. Cambridge University Press, Sweden
28. Koobus B and Farhat C (2004). A variational multiscale method for the large eddy simulation of compressible turbulent flows on unstructured meshes-application to vortex shedding. Comput Methods Appl Mech Eng 193: 1367-1383
29. Kravchenko AG, Moin P and Moser R (1996). Zonal embedded grids for numerical simulation of wall-bounded turbulent flows. J Comput Phys 127: 412-423
30. Kravchenko AG, Moin P and Shariff K (1999). B-spline method and zonal grids for simulation of complex turbulent flows. J Comput Phys 151: 757-789
31. Kwok WY, Moser RD and Jiménez J (2001). A critical evaluation of the resolution properties of B-spline and compact finite difference methods. J Comput Phys 174: 510-551
32. Lele SK (1992). Compact finite difference schemes with spectral-like resolution. J Comput Phys 103: 16-42
33. Masud A and Khurram RA (2004). A multiscale/stabilized finite element method for the advection-diffusion equation. Comput Methods Appl Mech Eng 193: 1997-2018
34. Moin P (2001). Fundamentals of engineering numerical analysis. Cambridge University Press, London
35. Moser R, Kim J and Mansour R (1999). DNS of turbulent channel flow up to Re = 590. Phys Fluids 11: 943-945
36. Piegl L and Tiller W (1997). The NURBS book (Monographs in visual communication), 2nd edn. Springer, New York
37. Rogers DF (2001). An introduction to NURBS with historical perspective. Academic, San Diego
38. Scovazzi G (2004) Multiscale methods in science and engineering. PhD thesis, Department of Mechanical Engineering, Stanford Universty. Available at http://www.cs.sandia.gov/~gscovaz
39. Shakib F, Hughes TJR and Johan Z (1991). A new finite element formulation for computational fluid dynamics: X. The compressible Euler and Navier-Stokes equations. Comput Methods Appl Mech Eng 89: 141-219
40. Shariff K and Moser RD (1998). Two-dimensional mesh embedding for B-spline methods. J Comput Phys 145: 471-488
41. Tezduyar TE (2003). Computation of moving boundaries and interfaces and stabilization parameters. Int J Numer Methods Fluids 43: 555-575
42. Tezduyar TE and Sathe S (2004). Enhanced-discretization space-time technique (EDSTT). Comput Methods Appl Mech Eng 193: 1385-1401
43. Tezduyar TE and Sathe S (2006). Enhanced-discretization selective stabilization procedure (EDSSP). Comput Mech 38: 456-468