The role of bulk viscosity in stabilized finite element formulations for incompressible flow: A review

Computer Methods in Applied Mechanics and Engineering

Volumn 163, Issue 1-4, 1998, Pages 1-10

  De Mulder, Tom ^a  

^a VON KARMAN INSTITUTE FOR FLUID DYNAMICS   (Belgium)

Author keywords

Incompressible flow; Viscosity

Indexed keywords

FINITE ELEMENT METHOD; GALERKIN METHODS; LEAST SQUARES APPROXIMATIONS; MATHEMATICAL MODELS; VISCOUS FLOW;

BULK VISCOSITY;

INCOMPRESSIBLE FLOW;

INCOMPRESSIBLE FLOW; VISCOSITY;

INCOMPRESSIBLE FLOW; VISCOSITY;

EID: 0032556079     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0045-7825(98)00015-2     Document Type: Review

References (19)

1. [1] T.J.R. Hughes, L.P. Franca and M. Balestra, A new FEM for CFD: V. Circumventing the Babuška-Brezzi condition: A stable Petrov-Galerkin formulation of the Stokes problem accommodating equal-order interpolations, Comput. Methods Appl. Mech. Engrg. 59 (1986) 85-99.
2. [2] L.P. Franca and T.J.R. Hughes, Two classes of mixed finite element methods, Comput. Methods Appl. Mech. Engrg. 69 (1988) 89-129.
3. [3] L.P. Franca and S.L. Frey, Stabilized finite element methods: II. The incompressible Navier-Stokes equations, Comput. Methods Appl. Mech. Engrg. 99 (1992) 209-233.
4. [4] L.P. Franca and T.J.R. Hughes, Convergence analyses of Galerkin least-squares methods for symmetric advective-diffusive forms of the Stokes and incompressible Navier-Stokes equations, Comput. Methods Appl. Mech. Engrg. 105 (1993) 285-298.
5. [5] P. Hansbo and A. Szepessy, A velocity-pressure streamline diffusion finite element method for the incompressible Navier-Stokes equations, Comput. Methods Appl. Mech. Engrg. 84 (1990) 175-192.
6. [6] M. Behr and T. Tezduyar, Finite element solution strategies for large-scale flow simulations, Comput. Methods Appl. Mech. Engrg. 112 (1994) 3-24.
7. [7] T.J.R. Hughes, Finite element methods for fluids, in: Proc. of the AGARD-VKI LS on Unstructured Grid Methods for Advection Dominated Flows, pp. 2.1-2.22, AGARD Report 787, 1992.
8. [8] T.J.R. Hughes and M. Mallet, A new finite element formulation for computational fluid dynamics: III. The generalized streamline operator for multidimensional advective-diffusive systems, Comput. Methods Appl. Mech. Engrg. 58 (1986) 305-328.
9. [9] M. Fortin and R. Glowinsky, Augmented Lagrangian Methods: Applications to the Numerical Solution of Boundary-Value Problems (North-Holland, 1983).
10. [10] O. Zienkiewicz and J. Wu, Incompressibility without tears - How to avoid restrictions of mixed formulation, Int. J. Numer. Methods Engrg. 32 (1991) 1189-1203.
11. [11] S. Idelsohn, M. Storti and N. Nigro, Stability analysis of mixed finite element formulations with special mention of equal-order interpolations, Int. J. Numer. Methods Fluids 20 (1995) 1003-1022.
12. [12] R. Bird, W. Stewart and E. Lightfoot, Transport Phenomena (J. Wiley & Sons, 1960).
13. [13] A.N. Brooks and T.J.R. Hughes, 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.
14. [14] J.-J. Droux and T.J.R. Hughes, A boundary integral modification of the Galerkin least squares formulation for the Stokes problem, Comput. Methods Appl. Mech. Engrg. 113 (1994) 173-182.
15. [15] A. Chorin, A numerical method for solving incompressible viscous flow problems, J. Comput. Phys. 2 (1967) 12-26.
16. [16] J. Ramshaw and V. Mousseau, Accelerated artificial compressibility method for steady-state incompressible flow calculations, Comput. Fluids. 18(4) (1990) 361-367.
17. [17] T. De Mulder and C. Benocci, Wiggle-free solution of the incompressible Navier-Stokes equations over a collocated mesh, Technical Note 179, von Karman Institute, 1991.
18. [18] D. Pelletier, A. Fortin and R. Camarero, Are FEM solutions of incompressible flows really incompressible? (or how simple flows can cause headaches!), Int. J. Numer. Methods Fluids 9 (1989) 99-112.
19. [19] A. Mizukami, Finite element analysis of the steady Navier-Stokes equations by a multiplier method, Int. J. Numer. Methods Fluids 5 (1985) 281-292.