A stabilized finite element method for incompressible viscous flows using a finite increment calculus formulation

Computer Methods in Applied Mechanics and Engineering

Volumn 182, Issue 3-4, 2000, Pages 355-370

  Oñate, Eugenio ^a  

^a INTERNATIONAL CENTER FOR NUMERICAL METHODS IN ENGINEERING CIMNE   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; DIFFERENTIAL EQUATIONS; DIFFERENTIATION (CALCULUS); GALERKIN METHODS; NAVIER STOKES EQUATIONS; PRESSURE; VELOCITY; VISCOUS FLOW;

FINITE INCREMENT CALCULUS FORMULATION; INCOMPRESSIBLE VISCOUS FLOWS;

FINITE ELEMENT METHOD;

FINITE ELEMENT METHOD; INCOMPRESSIBLE FLOW; VISCOUS FLOW;

FINITE ELEMENT METHOD; INCOMPRESSIBLE FLOW; VISCOUS FLOW;

EID: 0342264461     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0045-7825(99)00198-X     Document Type: Conference Paper

References (33)

1. O.C. Zienkiewicz, R.L. Taylor, The Finite Element Method, McGraw-Hill, vol. 1, 1989; vol. 2, 1991.
2. O.C. Zienkiewicz, R.L. Taylor, The Finite Element Method, McGraw-Hill, vol. 1, 1989; vol. 2, 1991.
3. R. Codina, A finite element model for incompressible flow problems, Ph.D. Thesis, Universitat Politécnica de Catalunya, Barcelona, June 1992.
4. Brooks A., Hughes T.J.R. Streamline upwind/Petrov-Galerkin formulation for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations. Comput. Methods Appl. Mech. Engrg. 32:1982;199-259.
5. Hughes T.J.R., Mallet M. A new finite element formulations for computational fluid dynamics: III. The generalized streamline operator for multidimensional advective-diffusive systems. Comp. Methods Appl. Mech. Engrg. 58:1986;305-328.
6. Hansbo P., Szepessy A. A velocity-pressure streamline diffusion finite element method for the incompressible Navier-Stokes equations. Comp. methods Appl. Mech. Engrg. 84:1990;175-192.
7. Hughes T.J.R., Franca L.P., Balestra M. A new finite element formulation for computational fluid dynamics. V Circumventing the Babuska-Brezzi condition: A stable Petrov-Galerkin formulation of the Stokes problem accomodating equal order interpolations. Comp. methods Appl. Mech. Engrg. 59:1986;85-89.
8. Franca L.P., Frey S.L. Stabilized finite element methods: II. The incompressible Navier-Stokes equations. Comput. methods Appl. Mech. Engrg. 99:1992;209-233.
9. T.J.R. Hughes, G. Hauke, K. Jansen, Stabilized finite element methods in fluids: Inspirations, origins, status and recent developments, in: T.J.R. Hughes, E. Oñate, O.C. Zienkiewicz (Eds.), Recent Developments in Finite Element Analysis (A Book Dedicated to Robert L. Taylor) International Center for Numerical Methods in Engineering, Barcelona, Spain, 1994, pp. 272-292.
10. Hughes T.J.R., Franca L.P., Hulbert G.M. A new finite element formulation for computational fluid dynamics: VIII. The Galerkin/least-squares method for advective-diffusive equations. Comput. methods Appl. Mech. Engrg. 73:1989;173-189.
11. Zienkiewicz O.C., Codina R. A general algorithm for compressible and incompressible flow. Part I: The split characteristic based scheme. Int. J. Num. Meth. Fluids. 20:1995;869-885.
12. Zienkiewicz O.C., Morgan K., Satya Sai B.V.K., Codina R., Vázquez M. A general algorithm for compressible and incompressible flow. Part II: Tests on the explicit form. Int. J. Num. Meth. Fluids. 20(8-9):1995;886-913.
13. Hughes T.J.R. Multiscale phenomena: Greens functions subgrid scale models, bubbles and the origins of stabilized methods. Comput. methods Appl. Mech. Engrg. 127:1995;387-401.
14. R. Codina, A stabilized finite element method for generalized stationary incompressible flows, Publication PI-148, CIMNE, Barcelona, February 1999.
15. Brezzi F., Bristeau M.O., Franca L.P., Mallet M., Rogé G. A relationship between stabilized finite element methods and the Galerkin method with bubble functions. Comput. methods Appl. Mech. Engrg. 96:1992;117-129.
16. F. Brezzi, D. Marini, A. Russo, Pseudo residual-free bubbles and stabilized methods, in: J. Periaux et al. (Eds.), Computational Methods in Applied Sciences, Wiley, Chichester, 1996.
17. F. Brezzi, L.P. Franca, T.J.R. Hughes, A. Russo, " b=∫g ", Comput. methods Appl. Mech. Engrg. 145 (1997) 329-339.
18. Mizakami A., Hughes T.J.R. A Petrov-Galerkin finite element method for convection dominated flows: an accurate upwinding technique for satisfying the maximum principle. Comput. methods Appl. Mech. Engrg. 50:1985;181-193.
19. Hughes T.J.R., Mallet M. A new finite element formulations for computational fluid dynamics: IV. A discontinuity capturing operator for multidimensional advective-diffusive system. Comput. methods Appl. Mech. Engrg. 58:1986;329-336.
20. Gale a o A.C., Dutra do Carmo E.G. A consistent approximate upwind Petrov-Galerkin method for convection dominated problems. Comput. methods Appl. Mech. Engrg. 68:1988;83-95.
21. Codina R. A discontinuity-capturing crosswind dissipation for the finite element solution of the convection-diffusion equation. Comput. methods Appl. Mech. Engrg. 110:1993;325-342.
22. Oñate E. On the stabilization of numerical solution for advective-diffusive transport and fluid flow problems. October 1996;Publication PI-81, CIMNE, Barcelona.
23. Oñate E. Derivation of stabilized equations for advective-diffusive transport and fluid flow problems. Comput. methods Appl. Mech. Engrg. 151(1/2):1998;233-267.
24. Oñate E., García J., Idelsohn S. Computation of the stabilization parameter for the finite element solution of advective-diffusive problems. Int. J. Num. Meth. Fluids. 25:1997;1385-1407.
25. E. Oñate, J. García, S. Idelsohn, An alpha-adaptive approach for stabilized finite element solution of advective-diffusive problems with sharp gradients, in: P. Ladeveze, J.T. Oden (Eds.), New Adv. Adaptive Comp. Met. Mech., Elsevier, New York, 1998.
26. Oñate E., Manzan M. A general procedure for deriving stabilized space-time finite element methods for advective-diffusive problems. July 1998;Publication PI-133, CIMNE, Barcelona.
27. F. Ilinca, J.F. Hétu, D. Peletier, On stabilized finite element formulations for incompressible advective-diffusive transport and fluid flow problems, AIAA-97-1863, Presented at AIAA CFD Conference, Snowman, USA, July 1997; Comp. methods Appl. Mech. Engrg., in press.
28. F. Ilinca, J.F. Hétu, D. Peletier, On stabilized finite element formulations for incompressible advective-diffusive transport and fluid flow problems, AIAA-97-1863, Presented at AIAA CFD Conference, Snowman, USA, July 1997; Comp. methods Appl. Mech. Engrg., in press.
29. Zienkiewicz O.C., Jain P.C., Oñate E. Flow of solids during forming and extrussion: some aspects of numerical solution. Int. J. Solids Struc. 14:1978;15-38.
30. Zienkiewicz O.C., Rojek J., Taylor R.L., Pastor M. Triangles and tetrahedra in explicit dynamic codes for solids. Int. J. Num. Meth. Engrg. 43:1998;565-583.
31. Oñate E., García J. A stabilized finite element method for incompressible flows involving free surface waves. 1999;Publication PI-160, CIMNE, Barcelona.
32. Zienkiewicz O.C., Zhu J.Z. The supercorvergent patch recovery (SPR) and adaptive finite element refinement. Comp. methods Appl. Mech. Engrg. 101:1992;207-224.
33. Wiberg N.E., Abdulwahab F., Li X.D. Error estimation and adaptive procedures based on superconvergent patch recovery. Archives Comput. meth. Engrg. 4(3):1997;203-242.