FEM simulation of non-stationary incompressible viscous fluids

Engineering Computations (Swansea, Wales)

Volumn 23, Issue 8, 2006, Pages 922-932

  Tralli, Aldo ^a   Gaudenzi, Paolo ^a  

^a SAPIENZA UNIVERSITY OF ROME   (Italy)

Author keywords

Finite difference methods; Finite element analysis; Simulation; Viscosity

Indexed keywords

BOUNDARY LAYER FLOW; COMPUTATIONAL FLUID DYNAMICS; COMPUTER SIMULATION; CONVERGENCE OF NUMERICAL METHODS; FINITE DIFFERENCE METHOD; FINITE ELEMENT METHOD; LAMINAR FLOW; NONLINEAR EQUATIONS; PRODUCT DESIGN;

COMPUTATIONAL REQUIREMENTS; FRACTIONAL-STEP METHODS; REAL LIFE APPLICATIONS; VORTICAL FLOWS;

VISCOUS FLOW;

EID: 33750689915     PISSN: 02644401     EISSN: None     Source Type: Journal    
DOI: 10.1108/02644400610707801     Document Type: Article

References (27)

1. Armaly, F., Durst, F., Pereira, J.C.F. and Schonung, B. (1983), "Experimental and theoretical investigation of backward facing step flow", Journal of Fluid Mechanics, Vol. 127, pp. 473-96.
2. Arnold, D.N., Brezzi, F. and Fortin, M. (1984), "A stable finite element for the stokes equations", Calcolo, Vol. 23, pp. 337-44.
3. Bathe, K.J. (1995), Finite Element Procedures, Prentice-Hall, Englewood Cliffs, NJ.
4. Bathe, K.J. and Zhang, H. (2002), "A flow-condition-based interpolation finite element procedure for incompressible fluid flows", Computers & Structures, Vol. 80, pp. 1267-77.
5. Brezzi, F. (1974), "On the existence, uniqueness and approximation of sadd-le point problems arising from Lagrangian multipliers", RAIRO, Vol. 8, pp. 129-51.
6. Brezzi, F. and Douglas, J. (1988), "Stabilized mixed methods for the Stokes problem", Num. Math., Vol. 53, pp. 225-35.
7. Brezzi, F. and Fortin, M. (1991), Mixed and Hybrid Finite Element Methods, Springer-Verlag, New York, NY.
8. Brezzi, F. and Pitkäranta, J. (1984), "On the stabilization of finite element approximations of the Stokes equations", in Hackbusch, W. (Ed.), Efficient Solutions of Elliptic Systems, Vieweg, Braunschweig, pp. 11-9.
9. Brooks, A.N. and Hughes, T.J.R. (1982), "Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations", Comput. Methods Appl. Mech. Eng., Vol. 32, pp. 199-259.
10. Brown, D.L., Cortez, R. and Minion, M.L. (2001), "Accurate projection methods for the incompressible Navier-Stokes equations", Journal of Computational Physics, Vol. 168, pp. 464-99.
11. Chorin, A.J. (1968), "Numerical solution of the Navier-Stokes equations", Math. Comput., Vol. 22.
12. Chorin, A.J. (1969), "On the convergence of discrete approximations to the Navier-Stokes equations", Math. Comput., Vol. 23.
13. Guermond, J.L. and Quartapelle, L. (1997), "Calculation of incompressible viscous flows by an unconditionally stable projection FEM", J. Comp. Phys., Vol. 132.
14. Hughes, T.J.R., Franca, L.P. and Balestra, M. (1986), "A new finite element formulation for computational fluid mechanics: V. Circumventing the Babuska-Brezzi condition: a stable Petrov-Galerkin formulation of the Stokes problem accommodating equal order interpolation", Comput. Methods Appl. Mech. Eng., Vol. 59, pp. 85-99.
15. Hughes, T.J.R., Franca, L.P. and Hulbert, G.M. (1989), "A new finite element formulation for computational fluid dynamics: VIII. The Galerkin/least-squares method for advective-diffusive equations", Comput. Methods Appl. Mech. Eng., Vol. 73 No. 2, pp. 173-89.
16. Johnson, C. and Pitkäranta, J. (1986), "An analysis of discontinuous Galerkin methods for scalar hyperbolic equations", Math. Comp., Vol. 46, pp. 1-26.
17. Kim, J. and Moin, P. (1985), "Application of a fractional-step method to incompressible Navier-Stokes equations", J. Comp. Phys., Vol. 59, pp. 308-14.
18. Orlandi, P. (1989), A Numerical Method for Direct Simulation of Turbulence in Complex Geometries, Annual Research Briefs, Stanford University, Stanford, CA, pp. 215-29.
19. Orlandi, P. (1999), Fluid Flow Phenomena: A Numerical Toolkit, Kluwer Academic Publishers, Dordrecht.
20. Perot, B. (1993), "An analysis of the fractional step method", Journal of Computational Physics, Vol. 108, pp. 51-8.
21. Pullin, D.I. and Perry, A.E. (1980), "Some flow visualization experiments on the starting vortex", J. Fluid Mech., Vol. 97, pp. 239-55.
22. Quarteroni, A., Saleri, F. and Veneziani, A. (1999), "Analysis of the Yosida method for the incompressible Navier-Stokes equations", J. Math. Pures Appl., Vol. 78.
23. Rai, M. and Moin, P. (1991), "Direct simulation of turbulent flow using finite difference schemes", J. Comput. Phys., Vol. 96.
24. Temam, R. (1969), "Sur l'approximation de la solution des equations de Navier-Stokes par la methode des pas fractionnaires, II", Arch. Rational Mech. Anal., Vol. 33.
25. Timmermans, L.J.P., Minev, P.D. and Van De Vosse, F.N. (1996), "An approximate projection scheme for incompressible flow using spectral elements", Int. J. Numer. Methods for Fluids, Vol. 22.
26. Tralli, A. (2005), "A FEM framework for fluid-structure interaction phenomena", PhD thesis.
27. Verzicco, R. and Orlandi, P. (1996), "A finite-difference scheme for three-dimensional incompressible flows in cylindrical coordinates", J. Comput. Phys., Vol. 123.