Finite elements in fluids: Special methods and enhanced solution techniques

Computers and Fluids

Volumn 36, Issue 2, 2007, Pages 207-223

  Tezduyar, Tayfun E ^a  

^a RICE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EQUATIONS OF MOTION; FINITE ELEMENT METHOD; FLOW OF FLUIDS; FLUID STRUCTURE INTERACTION; ITERATIVE METHODS; STABILITY;

INTERFACE-CAPTURING TECHNIQUE; INTERFACE-TRACKING TECHNIQUE; STABILIZED FORMULATION;

COMPUTATIONAL FLUID DYNAMICS;

COMPUTATIONAL FLUID DYNAMICS; EQUATIONS OF MOTION; FINITE ELEMENT METHOD; FLOW OF FLUIDS; FLUID STRUCTURE INTERACTION; ITERATIVE METHODS; STABILITY;

EID: 33750608917     PISSN: 00457930     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.compfluid.2005.02.010     Document Type: Review

References (59)

1. Tezduyar TE. Finite elements in fluids: stabilized formulations and moving boundaries and interfaces. Comput Fluids, in press, doi:10.1016/j.compfluid.2005.02.011.
2. Hughes T.J.R., and Brooks A.N. A multi-dimensional upwind scheme with no crosswind diffusion. In: Hughes T.J.R. (Ed). Finite element methods for convection dominated flows AMD-vol. 34 (1979), ASME, New York 19-35
3. Brooks A.N., and Hughes T.J.R. Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations. Comput Meth Appl Mech Eng 32 (1982) 199-259
4. Tezduyar TE, Hughes TJR. Development of time-accurate finite element techniques for first-order hyperbolic systems with particular emphasis on the compressible Euler equations. NASA Technical Report NASA-CR-204772, NASA, 1982.
5. Tezduyar TE, Hughes TJR. Finite element formulations for convection dominated flows with particular emphasis on the compressible Euler equations. In: Proceedings of AIAA 21st aerospace sciences meeting, AIAA Paper 83-0125, Reno, Nevada, 1983.
6. Hughes T.J.R., and Tezduyar T.E. Finite element methods for first-order hyperbolic systems with particular emphasis on the compressible Euler equations. Comput Meth Appl Mech Eng 45 (1984) 217-284
7. Donea J. A Taylor-Galerkin method for convective transport problems. Int J Numer Meth Eng 20 (1984) 101-120
8. Johnson C., Navert U., and Pitkäranta J. Finite element methods for linear hyperbolic problems. Comput Meth Appl Mech Eng 45 (1984) 285-312
9. Hughes T.J.R., Franca L.P., and Balestra M. A new finite element formulation for computational fluid dynamics: V. Circumventing the Babuška-Brezzi condition: a stable Petrov-Galerkin formulation of the Stokes problem accommodating equal-order interpolations. Comput Meth Appl Mech Eng 59 (1986) 85-99
10. Hughes T.J.R., Franca L.P., and Mallet M. A new finite element formulation for computational fluid dynamics: VI. Convergence analysis of the generalized SUPG formulation for linear time-dependent multi-dimensional advective-diffusive systems. Comput Meth Appl Mech Eng 63 (1987) 97-112
11. Hughes T.J.R., and Hulbert G.M. Space-time finite element methods for elastodynamics: formulations and error estimates. Comput Meth Appl Mech Eng 66 (1988) 339-363
12. Tezduyar T.E. Stabilized finite element formulations for incompressible flow computations. Adv Appl Mech 28 (1992) 1-44
13. Tezduyar T.E., Mittal S., Ray S.E., and Shih R. Incompressible flow computations with stabilized bilinear and linear equal-order-interpolation velocity-pressure elements. Comput Meth Appl Mech Eng 95 (1992) 221-242
14. Franca L.P., Frey S.L., and Hughes T.J.R. Stabilized finite element methods: I. Application to the advective-diffusive model. Comput Meth Appl Mech Eng 95 (1992) 253-276
15. Farhat C., Lesoinne M., and Maman N. Mixed explicit/implicit time integration of coupled aeroelastic problems: three-field formulation, geometric conservation and distributed solution. Int J Numer Meth Fluids 21 (1995) 807-835
16. Lohner R, Yang C, Baum JD. Rigid and flexible store separation simulations using dynamic adaptive unstructured grid technologies. In: Proceedings of the first AFOSR conference on dynamic motion CFD. New Brunswick, NJ, 1996.
17. Stein K., Benney R., Kalro V., Tezduyar T.E., Leonard J., and Accorsi M. Parachute fluid-structure interactions: 3-D computation. Comput Meth Appl Mech Eng 190 (2000) 373-386
18. Garcia J., Onate E., Sierra H., and Idelsohn S. A stabilized numerical method for analysis of ship hydrodynamics. Proceedings of ECCOMAS 1998 (1998), John Wiley
19. Onate E., Idelsohn S., Sacco C., and Garcia J. Stabilization of the numerical solution for the free surface wave equation in fluid dynamics. Proceedings of ECCOMAS 1998 (1998), John Wiley
20. Onate E, Garcia J. A methodology for analysis of fluid-structure interaction accounting for free surface waves. In: Proceedings of european conference on computational mechanics. Munich, Germany, 1999.
21. Cruchaga M., and Onate E. A generalized streamline finite element approach for the analysis of incompressible flow problems including moving surfaces. Comput Meth Appl Mech Eng 173 (1999) 241-255
22. Ohayon R, Felippa C. (Eds.), Advances in computational methods for fluid-structure interaction and coupled problems. Comput Meth Appl Mech Eng 2001;190.
23. Glowinski R. Finite element methods for incompressible viscous flow. In: Ciarlet P.G., and Lions J.L. (Eds). Handbook of numerical analysis vol. IX (2003), North-Holland, Amsterdam 3-1176 [Chapter 8-9]
24. Tezduyar T.E., Behr M., and Liou J. A new strategy for finite element computations involving moving boundaries and interfaces-the deforming-spatial-domain/space-time procedure: I. The concept and the preliminary numerical tests. Comput Meth Appl Mech Eng 94 (1992) 339-351
25. Tezduyar T.E., Behr M., Mittal S., and Liou J. A new strategy for finite element computations involving moving boundaries and interfaces-the deforming-spatial-domain/space-time procedure: II. Computation of free-surface flows, two-liquid flows, and flows with drifting cylinders. Comput Meth Appl Mech Eng 94 (1992) 353-371
26. Tezduyar T.E., Behr M., Mittal S., and Johnson A.A. Computation of unsteady incompressible flows with the finite element methods-space-time formulations, iterative strategies and massively parallel implementations. New methods in transient analysis PVP-vol. 246/AMD-vol. 143 (1992), ASME, New York 7-24
27. Tezduyar T., Aliabadi S., Behr M., Johnson A., Kalro V., and Litke M. Flow simulation and high performance computing. Comput Mech 18 (1996) 397-412
28. Behr M., and Tezduyar T. The shear-slip mesh update method. Comput Meth Appl Mech Eng 174 (1999) 261-274
29. Behr M., and Tezduyar T. Shear-slip mesh update in 3D computation of complex flow problems with rotating mechanical components. Comput Meth Appl Mech Eng 190 (2001) 3189-3200
30. Tezduyar T.E. Finite element methods for flow problems with moving boundaries and interfaces. Arch Comput Meth Eng 8 (2001) 83-130
31. Tezduyar T.E. Finite element methods for fluid dynamics with moving boundaries and interfaces. In: Stein E., De Borst R., and Hughes T.J.R. (Eds). Encyclopedia of computational mechanics, vol. 3: Fluids (2004), John Wiley & Sons [Chapter 17]
32. Tezduyar T.E. Stabilized finite element methods for computation of flows with moving boundaries and interfaces. Lecture notes on finite element simulation of flow problems (basic-advanced course) (2003), Japan Society of Computational Engineering and Sciences, Tokyo, Japan
33. Tezduyar T.E. Moving boundaries and interfaces. In: Franca L.P., Tezduyar T.E., and Masud A. (Eds). Finite element methods: 1970's and beyond (2004), CIMNE, Barcelona, Spain 205-220
34. Tezduyar TE. Interface-tracking and interface-capturing techniques for finite element computation of moving boundaries and interfaces, Comput Meth Appl Mech Eng, in press.
35. Tezduyar T., Aliabadi S., and Behr M. Enhanced-discretization interface-capturing technique. In: Matsumoto Y., and Prosperetti A. (Eds). ISAC'97 high performance computing on multiphase flows (1997), Japan Society of Mechanical Engineers 1-6
36. Tezduyar T., Aliabadi S., and Behr M. Enhanced-discretization interface-capturing technique (EDICT) for computation of unsteady flows with interfaces. Comput Meth Appl Mech Eng 155 (1998) 235-248
37. Mittal S., Aliabadi S., and Tezduyar T. Parallel computation of unsteady compressible flows with the EDICT. Comput Mech 23 (1999) 151-157
38. Tezduyar T., Osawa Y., Stein K., Benney R., Kumar V., and McCune J. Computational methods for parachute aerodynamics. In: Hafez M., Morinishi K., and Periaux J. (Eds). Computational fluid dynamics for the 21st century (2001), Springer
39. Tezduyar T. Finite element interface-tracking and interface-capturing techniques for flows with moving boundaries and interfaces. In: Proceedings of the ASME symposium on fluid-physics and heat transfer for macro- and micro-scale gas-liquid and phase-change flows (CD-ROM), ASME Paper IMECE2001/HTD-24206, ASME, New York, 2001.
40. Tezduyar T.E. Stabilized finite element formulations and interface-tracking and interface-capturing techniques for incompressible flows. In: Hafez M.M. (Ed). Numerical simulations of incompressible flows (2003), World Scientific, New Jersey 221-239
41. Tezduyar T. Interface-tracking and interface-capturing techniques for computation of moving boundaries and interfaces. In: Proceedings of the fifth world congress on computational mechanics, On-line publication: http://wccm.tuwien.ac.at/, Paper-ID: 81513, Vienna, Austria, 2002.
42. Tezduyar T.E., and Sathe S. Enhanced-discretization space-time technique (EDSTT). Comput Meth Appl Mech Eng 193 (2004) 1385-1401
43. Tezduyar T.E., and Sathe S. Enhanced-approximation linear solution technique (EALST). Comput Meth Appl Mech Eng 193 (2004) 2033-2049
44. Tezduyar T., Aliabadi S., Behr M., Johnson A., Kalro V., and Litke M. High performance computing techniques for flow simulations. In: Papadrakakis M. (Ed). Solving large-scale problems in mechanics: parallel solution methods in computational mechanics (1997), John Wiley & Sons 363-398 [Chapter 10]
45. Johan Z., Hughes T.J.R., and Shakib F. A globally convergent matrix-free algorithm for implicit time-marching schemes arising in finite element analysis in fluids. Comput Meth Appl Mech Eng 87 (1991) 281-304
46. Johan Z., Mathur K.K., Johnsson S.L., and Hughes T.J.R. A case study in parallel computation: viscous flow around an Onera M6 wing. Int J Numer Meth Fluids 21 (1995) 877-884
47. Tezduyar T.E. Stabilized finite element methods for flows with moving boundaries and interfaces. HERMIS: Int J Comput Math Appl 4 (2003) 63-88
48. Tezduyar TE, Sathe S, Keedy R, Stein K. Space-time finite element techniques for computation of fluid-structure interactions. Comput Meth Appl Mech Eng, in press.
49. Tezduyar T.E., and Sathe S. Enhanced-discretization successive update method (EDSUM). Int J Numer Meth Fluids 47 (2005) 633-654
50. Benek JA, Buning PG, Steger JL. A 3-D chimera grid embedding technique, Paper 85-1523, AIAA, 1985.
51. Hirt C.W., and Nichols B.D. Volume of fluid (VOF) method for the dynamics of free boundaries. J Comput Phys 39 (1981) 201-225
52. Saad Y., and Schultz M. GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J Sci Statist Comput 7 (1986) 856-869
53. Tezduyar T.E., Behr M., Aliabadi S.K., Mittal S., and Ray S.E. A new mixed preconditioning method for finite element computations. Comput Meth Appl Mech Eng 99 (1992) 27-42
54. Kalro V., and Tezduyar T. Parallel iterative computational methods for 3D finite element flow simulations. Comp Assist Mech Eng Sci 5 (1998) 173-183
55. Tezduyar TE. Interface-tracking, interface-capturing and enhanced solution techniques. In: Proceedings of the first South-American congress on computational mechanics (CD-ROM), Santa Fe-Parana, Argentina, 2002.
56. Tezduyar TE. Adaptive determination of the finite element stabilization parameters. In: Proceedings of the ECCOMAS computational fluid dynamics conference 2001 (CD-ROM), Swansea, Wales, United Kingdom, 2001.
57. Tezduyar T.E. Computation of moving boundaries and interfaces and stabilization parameters. Int J Numer Meth Fluids 43 (2003) 555-575
58. Tezduyar T. Stabilization parameters and local length scales in SUPG and PSPG formulations. In: Proceedings of the fifth world congress on computational mechanics, On-line publication: http://wccm.tuwien.ac.at/, Paper-ID: 81508, Vienna, Austria, 2002.
59. Hughes T.J.R. The finite element method. Linear static and dynamic finite element analysis (1987), Prentice-Hall, Englewood Cliffs, NJ