Convergence of finite element approximations of large eddy motion

Numerical Methods for Partial Differential Equations

Volumn 18, Issue 6, 2002, Pages 689-710

  Iliescu, Traian ^a   John, Volker ^b   Layton, William J ^c  

^a ARGONNE NATIONAL LABORATORY   (United States)

^b OTTO VON GUERICKE UNIVERSITY   (Germany)

^c UNIVERSITY OF PITTSBURGH   (United States)

Author keywords

Finite element method; Large eddy simulation; Navier Stokes equations

Indexed keywords

EID: 0036842539     PISSN: 0749159X     EISSN: None     Source Type: Journal    
DOI: 10.1002/num.10027     Document Type: Article

References (52)

1. P. Galdi and W. Layton, Approximation of the larger eddies in fluid motion ii: A model for space filtered flow, Math Models Meth Appl Sci 10(3) (2000), 343-350.
2. T. Iliescu and W. J. Layton, Approximating the larger eddies in fluid motion iii: the Boussinesq model for turbulent fluctuations, An St Univ "Al I Cuza" Iaşi, 44 (1998), 245-261.
3. R. Lewandowski, Analyse Mathematique et Oceanographie, Massen, 1997.
4. J. S. Smagorinsky, General circulation experiments with the primitive equations, Mon Weather Rev 91 (1963), 99-164.
5. W. J. Layton, A nonlinear, subgridscale model for incompressible viscous flow problems, SIAM J Sci Comput 17(2) (1996), 347-357.
6. W. J. Layton, Subgridscale modelling and finite element methods for the Navier Stokes equations, Report mbi-96-4, Otto-von-Guericke Universität, Magdeburg, Germany, 1996.
7. M. Germano, U. Piomelli, P. Moin, and W. Cabot, A dynamic subgrid-scale eddy viscosity model, Phys Fluids A 3 (1991), 1760-1765.
8. T. J. Hughes, L. Mazzei, and K. E. Jansen, Large eddy simulation and the variational multiscale method, Comput Visual Sci 3 (2000), 47-59.
9. P. Sagaut, Large eddy simulation for incompressible flows, Springer-Verlag, Berlin, Heidelberg, New York, 2001.
10. V. John, W. J. Layton, and N. Sahin, Derivation and analysis of near wall models for channel and recirculating flows, Technical Report, University of Pittsburgh, 2002, submitted.
11. P. M. Gresho and R. L. Sani, Incompressible Flow and the Finite Element Method, Wiley, New York, 2000.
12. A. Leonard, Energy cascade in large eddy simulation of turbulent fluid flows, Adv Geophysics 18A (1974), 237-248.
13. R. A. Clark, J. H. Ferziger, and W. C. Reynolds, Evaluation of subgrid-scale models using an accurately simulated turbulent flow, J Fluid Mech 91 (1979), 1-16.
14. A. A. Aldama, Filtering techniques for turbulent flow simulation, Vol. 56 of Springer Lecture Notes in English, Springer, Berlin, 1990.
15. M. E. Cantekin, J. J. Westerink, and R. A. Luettich, Jr., Low and moderate Reynolds number transient flow simulations using space filtered Navier-Stokes equations, Num Meth Part Diff Equ 10 (1994), 491-524.
16. J. Heywood and R. Rannacher, Finite element approximation of the nonstationary Navier-Stokes problem i: Regularity of solutions and second order error estimates for spatial discretization, SIAM J Num Anal 19 (1982), 275-311.
17. J. Heywood and R. Rannacher, Finite element approximation of the nonstationary Navier-Stokes problem iii: Smoothing property and higher order estimates for spatial discretization, SIAM J Num Anal 25 (1988), 489-512.
18. W. J. Layton, Weak imposition of "no-slip" conditions in finite element methods, Comput Math Appl 38 (1999), 129-142.
19. A. Liakos, Weak imposition of boundary conditions in the Stokes and Navier-Stokes equation, PhD thesis, Univ. of Pittsburgh, 1999.
20. Q. Du and M. D. Gunzburger, Finite-element approximations of a Ladyzhenskaya model for stationary incompressible viscous flow, SIAM J Numer Anal 27 (1990), 1-19.
21. T. Iliescu, Genuinely nonlinear models for convection-dominated problems, Preprint ANL/MCS-P857-1100, Argonne National Laboratory, 2000, submitted.
22. V. John and W. J. Layton, Analysis of numerical errors in large eddy simulation, SIAM J Numer Anal 2002, accepted for publication.
23. G. P. Galdi, An introduction to the mathematical theory of the Navier-Stokes equations, Vol. I: Linearized theory, Vol. 38 of Springer tracts in natural philosophy, Springer-Verlag, New York, 1994.
24. P. Coletti, A global existence theorem for large eddy simulation turbulence model, Math Models Meth Appl Sci 7 (1997), 579-591.
25. P. Coletti, Analytic and numerical results for k - ∈ and large eddy simulation turbulence models, PhD thesis, University of Trento, 1998.
26. L. G. Berselli, G. P. Galdi, T. Iliescu, and W. J. Layton, Mathematical analysis for the rational large eddy simulation model, Math Models Meth Appl Sci 12(8) (2002), 1-22.
27. O. A. Ladyzhenskaya, New equations for the description of motion of viscous incompressible fluids and solvability in the large of boundary value problems for them, Proc Steklov Inst Math 102 (1967), 95-118.
28. O. Axelsson and W. J. Layton, Defect correction methods for convection dominated convection diffusion methods, RAIRO Anal Numer 24 (1990), 423-455.
29. M. M. Vainberg, Variational methods and the method of monotone operators in the theory of nonlinear equations, Wiley, New York, 1973.
30. V. Girault and P. A. Raviart, Finite element approximation of the Navier-Stokes equations, Springer-Verlag, Berlin, Heidelberg, New York, 1979.
31. M. Gunzburger, Finite element methods for viscous incompressible flows, Academic Press, Boston, 1989.
32. G. Minty, Monotone (nonlinear) operators in Hubert space, Duke Math J 29 (1962), 341-346.
33. J. L. Lions, Quelques Méthodes de Résolution des Problèmes aux Limites Non Linéaires, Dunod, Gauthier-Villars, Paris, 1969.
34. G. Duvaut and J. L. Lions, Les Inéquations en Méchanique et Physique, Dunod, Paris, 1972.
35. 2-projection onto finite element function spaces, Math Comp 48 (1987), 521-523.
36. J. Xu, Theory of multilevel methods, PhD thesis, Cornell University, Ithaca, NY, 1989.
37. W. J. Layton, Analysis of a scale-similarity model of the motion of large eddies in turbulent flows, J Math Anal Appl 264 (2001), 546-559.
38. W. J. Layton and L. Tobiska, A two-level method with backtracking for the Navier-Stokes equations, SIAM J Numer Anal 35(5) (1998), 2035-2054.
39. M. O. Bristeau, R. Glowinski, and J. Periaux, Numerical methods for the Navier-Stokes equations: Applications to the simulation of compressible and incompressible viscous flows, Comput Phys Reports 6 (1987), 73-187.
40. P. Kloucek and F. S. Rys, Stability of the fractional step θ-scheme for the nonstationary Navier-Stokes equations, SIAM Num Anal 31 (1994), 1312-1335.
41. S. Turek, Efficient solvers for incompressible flow problems: an algorithmic and computational approach, Vol. 6 of Lecture notes in computational science and engineering, Springer, 1999.
42. R. Rannacher, Finite element methods for the incompressible Navier-Stokes equations, G. P. Galdi, J. G. Heywood, and R. Rannacher, editors, Fundamental directions in mathematical fluid dynamics, Birkhäuser, 2000, pp. 191-293.
43. M. Fortin, Finite element solution of the Navier-Stokes equations, Acta Numerica (1993), 239-284.
44. V. John and G. Matthies, Higher order finite element discretizations in a benchmark problem for incompressible flows, Int J Num Meth Fluids 37 (2001), 885-901.
45. V. John, Higher order finite element methods and multigrid solvers in a benchmark problem for the 3D Navier-Stokes equations, Int J Num Meth Fluids 2002, accepted for publication.
46. Y. Saad, Iterative methods for sparse linear systems, PWS Publishing Company, 1996.
47. V. John and L. Tobiska, Smoothers in coupled multigrid methods for the parallel solution of the incompressible Navier-Stokes equations, Int J Num Meth Fluids 33 (2000), 453-473.
48. A. J. Chorin, Numerical solution for the Navier-Stokes equations, Math Comp 22 (1968), 745-762.
49. D. Tafti, Comparison of some upwind-biased high-order formulations with a second-order central-difference scheme for time integration of the incompressible Navier-Stokes equations, Comp Fluids 25 (1996), 647-665.
50. V. John, Slip with friction and penetration with resistance boundary conditions for the Navier-Stokes equations - numerical tests and aspects of the implementation, J Comp Appl Math 2002, accepted for publication.
51. T. Iliescu, V. John, W. J. Layton, G. Matthies, and L. Tobiska, A numerical study of a class of les models, Int J Comput Fluid Dyn 2002, accepted for publication.
52. J. G. Heywood, R. Rannacher, and S. Turek, Artificial boundaries and flux and pressure conditions for the incompressible Navier-Stokes equations, Int J Numer Methods Fluids 22(5) (1996), 325-352.