Parallel finite element computation of unsteady incompressible flows

International Journal for Numerical Methods in Fluids

Volumn 26, Issue 1, 1998, Pages 17-37

  Wasfy, Tamer ^a   West, Alan C ^a   Modi, Vijay ^a  

^a Columbia University ^*  (United States)

Author keywords

Galerkin approximation; Incompressible Navier Stokes; Parallel finite element method

Indexed keywords

APPROXIMATION THEORY; COMPRESSIBLE FLOW; COMPUTATIONAL METHODS; FINITE ELEMENT METHOD; NAVIER STOKES EQUATIONS; REYNOLDS NUMBER;

INCOMPRESSIBLE FLOW;

UNSTEADY FLOW;

FINITE ELEMENT ANALYSIS; INCOMPRESSIBLE FLOW; NAVIER-STOKES EQUATIONS; UNSTEADY FLOW;

FINITE ELEMENT METHOD; INCOMPRESSIBLE; NAVIER-STOKES EQUATIONS; UNSTEADY FLOW;

EID: 0031947266     PISSN: 02712091     EISSN: None     Source Type: Journal    
DOI: 10.1002/(sici)1097-0363(19980115)26:1<17::aid-fld619>3.0.co;2-g     Document Type: Article

References (37)

1. P. F. Fischer and A. T. Patera, 'Parallel simulation of viscous incompressible flows', Ann. Rev. Fluid Mech., 26, 483-527 (1994).
2. O. C. Zienkiewicz and J. Wu, 'General explicit or semi-explicit algorithm for compressible and incompressible flows', Int. j. numer. meth. engng., 35, 457-479 (1992).
3. C. Farhat and L. Crivelli, 'Large scale FE parallel nonlinear computations using a homotopy method', in G. Rodrigue (ed.), SIAM, Philadelphia, PA, 1988, pp. 265-269.
4. C. Farhat and L. Crivelli, 'A general approach to nonlinear FE computations on shared memory multiprocessors', Comput. Meth. Appl. Mech. Engng., 72, 153-172 (1989).
5. M. E. 'Applications of parallel computing in computational fluid dynamics: a review', in H. Tyrar (ed.) Advances in Distributed Memory and Parallel Processing, Vol. 1, 1993.
6. N. M. Newmark, 'A method of computation for structural dynamics', J. Engng. Mech. Div. ASCE, 85, 67-94 (1959).
7. I. Babuska, 'Error bounds for finite element method', Numer. Math., 16, 322-333 (1971).
8. F. Brezzi, 'On the existence, uniqueness and approximation of saddle point problems arising from Lagrange multipliers', RAIRO, Ser. Rouge Anal. Numer, 8, (1976).
9. T. J. R. Hughes, W. K. Liu and A. Brooks, 'Finite element analysis of incompressible viscous flows by the penalty function formulation', J. Comput. Phys., 30, 1-60 (1979).
10. R. L. Lee, P. M. Gresho and R. L. Sani, 'Numerical smoothing techniques applied to some finite element solutions of the Navier-Stokes equations', Int. j. for numer. meth. engng., (1979)
11. T. J. R. Hughes, L. P. Franca and M. Mallet, 'A new finite element formulation for computational fluid dynamics: I. Symmetric forms of the compressible Euler and Navier Stokes equations and the second law of thermodynamics', Comput. Meth. Appl. Mech. Engng., 54, 223-234 (1986).
12. T. J. R. Hughes, L. P. Franca and M. Balestra, 'A new finite element formulation for computational fluid dynamics: V. Circumventing the Babuska-Brezzi condition: a stable Petrov-Galerkin formulation of the Stokes problem accommodating equal-order interpolations', Comput. Meth. Appl. Mech. Engng., 59, 85-99 (1986).
13. T. J. R. Hughes, L. P. Franca and Hulbert, 'A new finite element formulation for computational fluid dynamics: VIII. The Galerkin/least-squares method for advective-diffusive equations', Comput. Meth. Appl. Mech. Engng., 73, 173-189 (1989).
14. P. Hansbo and Szepessy, 'A velocity-pressure streamline diffusion finite element method for the incomrpessible Navier-Stokes equations', Comput. Meth. Appl. Mech. Engng., 84, 175-192 (1990).
15. L. P. Franca, T. J. R. Hughes, et al., 'Stabilized finite element methods: I. Application to the advective-diffusive model', Comput. Meth. Appl. Mech. Engng., 95, 253-276 (1992).
16. T. E. Tezduyar, S. Mittal, S. E. Ray and R. Shih, 'Incompressible flow computations with stabilized bilinear and linear equal-order-interpolation velocity-pressure elements', Comput. Meth. Appl. Mech. Engng., 95, 221-242 (1992).
17. J. Donea, 'A Taylor-Galerkin method for convective transport problems', Int. j. numer. meth. engng., 20, 101-119 (1984).
18. J. Donea, T. Belytschko and P. Smolinski, 'A generalized Galerkin method for steady convection-diffusion problems with application to quadratic shape function elements', Comput. Meth. Appl. Mech. Engng., 48, 25-43 (1985).
19. J. J. R. Tamaddon, P. Townsend and M. F. Webster, 'Numerical solution of unsteady viscous flows', Comput. Meth. Appl. Mech. Engng., 95, 301-315 (1992).
20. A. J. Chorin, 'A numerical method for solving incompressible viscous flow problems', J. Comput. Phys., 2, (1967).
21. J. T. Oden, Optimal h-p finite element methods', Comput. Meth. Appl. Mech. Engng., 112, 309-331 (1994).
22. T. J. R. Hughes and T. E. Tezduyar, 'Finite element methods for first-order hyperbolic systems with particular emphasis on the compressible Euler equations', Comput. Meth. Appl. Mech. Engng., 45, 217-284 (1984).
23. A. N. Brooks and T. J. R. Hughes, 'Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on incompressible Navier-Stokes equations', Comput. Meth. Appl. Mech. Eng., 32, 199-259 (1982).
24. J. C. Heinrich and O. C. Zienkiewicz, 'The finite element method and "upwinding" technique in the numerical solution of convection dominated problems', ASME Winter Ann. Meet., Finite Element Methods in Convection Dominated Flows, ASME, New York, 1979.
25. I. Christie and A. R. Mitchell, 'Upwinding of high order Galerkin methods in conduction-convection problems', Int. j. numer. meth. eng., 12, 1764-1771 (1978).
26. K. J. Bathe, Finite Element Procedures in Engineering Analysis, Prentice-Hall, Englewood Cliffs, NJ, 1982.
27. Z. Johan, K. K. Mathur, S. L. Johnsson and T. J. R. Hughes, 'Scalability of finite element applications on distributed-memory parallel computers', Comput. Meth. Appl. Mech. Engng., 119, 61-72 (1994).
28. O. C. Zienkiewicz and R. L. Taylor, The Finite Element Method, 4th edn, McGraw-Hill, New York, 1989.
29. A. J. Baker, Finite Element Computational Fluid Mechanics, McGraw-Hill, New York, 1983.
30. J. C. Heinrich and O. C. Zienkiwicz, 'Quadratic finite element schemes for two-dimensional convective transport problems', Int. j. numer. meth. engng., 11, 1831-1844 (1977).
31. M. Bercovier and M. Engelman, 'A finite element for the numerical solution of viscous incompressible flows', J. Comput. Phys., 30, 181-201 (1979).
32. J. C. Heinrich, 'On quadratic elements in finite element solutions of steady state convection-diffusion equation', Int. j. numer. meth. engng., 15, 1041-1052 (1980).
33. R. Codina, O. Eugenio and M. Cervera, 'The intrinsic time for the streamline upwind/Petrov-Galerkin formulation using quadratic elements', Comput. Meth. Appl. Mech. Eng., 94, 239-262 (1992).
34. B. F. Armaly, F. Durst, J. C. Pereira and M. Yianneskis, 'Experimental and theoretical investigation of backward-facing step bow', J. Fluid Mech., 127, 473-496 (1983).
35. R. Iwatsu, J. M. Hyun and K. Kuwahara, 'Numerical simulation of flows driven by a torsionally oscillating lid in a square cavity', J. Fluids Engng., 114, 143-151 (1992).
36. A. Roshko, On the development of turbulent wakes from vortex streets', NACA TN 2913, 1953.
37. M. O. Bristeau, M. Mallet, J. Perriaux and G. Roge, 'Development of finite element method for compressible flow simulations in aerospace design', AIAA Paper 90-0403, 1990.