Finite calculus formulations for finite element analysis of incompressible flows. Eulerian, ALE and Lagrangian approaches

Computer Methods in Applied Mechanics and Engineering

Volumn 195, Issue 23-24, 2006, Pages 3001-3037

  Onate E ^a   Garcia J ^a   Idelsohn, S R ^a   Del Pin, F ^a  

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

Author keywords

Finite calculus; Finite element method; Fluid structure interaction; Incompressible fluid; Lagrangian flow; Particle finite element method; Stabilized formulation

Indexed keywords

DIFFERENTIATION (CALCULUS); EQUATIONS OF MOTION; FINITE ELEMENT METHOD; FLUID STRUCTURE INTERACTION; INCOMPRESSIBLE FLOW;

FINITE CALCULUS; FLUID FLOW EQUATIONS; INCOMPRESSIBLE FLUID FLOW ANALYSIS; LAGRANGIAN FLOW;

COMPUTATIONAL FLUID DYNAMICS;

COMPUTATIONAL FLUID DYNAMICS; DIFFERENTIATION (CALCULUS); EQUATIONS OF MOTION; FINITE ELEMENT METHOD; FLUID STRUCTURE INTERACTION; INCOMPRESSIBLE FLOW;

EID: 33645073927     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2004.10.016     Document Type: Article

References (70)

1. O.C. Zienkiewicz R.C. Taylor The Finite Element Method fifth ed., 3 vols. 2000 Butterworth-Heinemann
2. C. Hirsch, Numerical Computation of Internal and External Flow, John Wiley, vol. 1, 1988, vol. 2, 1990.
3. A.J. Chorin A numerical solution for solving incompressible viscous flow problems J. Comp. Phys. 2 1967 12-26
4. W.R. Briley S.S. Neerarambam D.L. Whitfield Multigrid algorithm for three-dimensional incompressible high-Reynolds number turbulent flows AIAA J. 33 1 1995 2073-2079
5. J. Peraire K. Morgan J. Peiro The simulation of 3D incompressible flows using unstructured grids D.A. Caughey M.M. Hafez Frontiers of Computational Fluid Dynamics 1994 John Wiley (Chapter 16)
6. C. Sheng L.K. Taylor D.L. Whitfield Implicit lower-upper/ approximate-factorization schemes for incompressible flows J. Computat. Phys. 128 1 1996 32-42
7. M. Storti N. Nigro S.R. Idelsohn Steady state incompressible flows using explicit schemes with an optimal local preconditioning Comput. Methods Appl. Mech. Engrg. 124 1995 231-252
8. J.C. Heinrich P.S. Hayakorn O.C. Zienkiewicz An upwind finite element scheme for two dimensional convective transport equations Int. J. Numer. Methods Engrg. 11 1977 131-143
9. S.R. Idelsohn M. Storti N. Nigro Stability analysis of mixed finite element formulation with special mention to stabilized equal-order interpolations Int. J. Numer. Methods Fluids 20 1995 1003-1022
10. S.R. Idelsohn N. Nigro M. Storti G. Buscaglia A Petrov-Galerkin formulation for advection-reaction-diffusion Comput. Methods Appl. Mech. Engrg. 136 1996 27-46
11. A. Brooks T.J.R. Hughes 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
12. T.J.R. Hughes M. Mallet A new finite element formulations for computational fluid dynamics: III. The generalized streamline operator for multidimensional advective-diffusive systems Comput Methods Appl. Mech. Engrg. 58 1986 305-328
13. P. Hansbo 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
14. T.J.R. Hughes L.P. Franca 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. Methods Appl. Mech. Engrg. 59 1986 85-99
15. L.P. Franca S.L. Frey Stabilized finite element methods: II. The incompressible Navier-Stokes equations Comput. Methods Appl. Mech. Engrg. 99 1992 209-233
16. T.J.R. Hughes G. Hauke K. Jansen Stabilized finite element methods in fluids: Inspirations, origins, status and recent developments R.L. Taylor T.J.R. Hughes E. Oñate O.C. Zienkiewicz Recent Developments in Finite Element Analysis 1994 International Center for Numerical Methods in Engineering Barcelona, Spain 272-292
17. M.A. Cruchaga E. Oñate A finite element formulation for incompressible flow problems using a generalized streamline operator Comput. Methods Appl. Mech. Engrg. 143 1997 49-67
18. M.A. Cruchaga E. Oñate A generalized streamline finite element approach for the analysis of incompressible flow problems including moving surfaces Comput. Methods Appl. Mech. Engrg. 173 1999 241-255
19. T.J.R. Hughes L.P. Franca G.M. Hulbert 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
20. T.E. Tezduyar S. Mittal S.E. Ray R. Shih Incompressible flow computations with stabilized bilinear and linear equal order interpolation velocity-pressure elements Comput. Methods Appl. Mech. Engrg. 95 1992 221-242
21. J. Donea A Taylor-Galerkin method for convective transport problems Int. J. Numer. Methods Engrg. 20 1984 101-119
22. J. Douglas T.F. Russell Numerical methods for convection dominated diffusion problems based on combining the method of characteristics with finite element or finite difference procedures SIAM J. Numer. Anal. 19 1982 871
23. O. Pironneau On the transport-diffusion algorithm and its applications to the Navier-Stokes equations Numer. Math. 38 1982 309
24. R. Löhner K. Morgan O.C. Zienkiewicz The solution of non-linear hyperbolic equation systems by the finite element method Int. J. Numer. Methods Fluids 4 1984 1043
25. R. Codina M. Vazquez O.C. Zienkiewicz A general algorithm for compressible and incompressible flow-Part III. The semi-implicit form Int. J. Numer. Methods Fluids 27 1998 13-32
26. R. Codina O.C. Zienkiewicz CBS versus GLS stabilization of the incompressible Navier-Stokes equations and the role of the time step as stabilization parameter Commun. Numer. Methods Engrg. 18 2 2002 99-112
27. R. Codina J. Blasco Stabilized finite element method for the transient Navier-Stokes equations based on a pressure gradient operator Comput. Methods Appl. Mech. Engrg. 182 2000 277-301
28. T.J.R. Hughes Multiscale phenomena: Green functions, subgrid scale models, bubbles and the origins of stabilized methods Comput. Methods Appl. Mech. Engrg. 127 1995 387-401
29. F. Brezzi L.P. Franca T.J.R. Hughes A. Russo b = ∫g Comput. Methods Appl. Mech. Engrg. 145 1997 329-339
30. R. Codina Stabilized finite element approximation of transient incompressible flows using orthogonal subscales Comput. Methods Appl. Mech. Engrg. 191 2002 4295-4321
31. J. Donea A. Huerta Finite Element Method for Flow Problems 2003 John Wiley
32. E. Oñate Derivation of stabilized equations for advective-diffusive transport and fluid flow problems Comput. Methods Appl. Mech. Engrg. 151 1998 233-267
33. E. Onãte J. García S. Idelsohn Computation of the stabilization parameter for the finite element solution of advective-diffusive problems Int. J. Numer. Methods Fluids 25 1997 1385-1407
34. E. Oñate J. García S. Idelsohn An alpha-adaptive approach for stabilized finite element solution of advective-diffusive problems with sharp gradients P. Ladeveze J.T. Oden New Adv. Adaptive Comput. Methods Mech. 1998 Elsevier
35. E. Oñate M. Manzan A general procedure for deriving stabilized space-time finite element methods for advective-diffusive problems Int. J. Numer. Methods Fluids 31 1999 203-221
36. E. Oñate M. Manzan Stabilization techniques for finite element analysis of convection diffusion problems G. Comini B. Sunden Computational Analysis of Heat Transfer 2000 WIT Press Southampton
37. E. Oñate A stabilized finite element method for incompressible viscous flows using a finite increment calculus formulation Comput. Methods Appl. Mech. Engrg. 182 1-2 2000 355-370
38. E. Oñate J. García A finite element method for fluid-structure interaction with surface waves using a finite calculus formulation Comput. Methods Appl. Mech. Engrg. 191 2001 635-660
39. E. Oñate Possibilities of finite calculus in computational mechanics Int. J. Numer. Comput. Methods Engrg. 60 1 2004 255-281
40. J. García E. Oñate An unstructured finite element solver for ship hydrodynamic problems J. Appl. Mech. 70 January 2003 18-26
41. E. Oñate J. García S.R. Idelsohn Ship hydrodynamics E. Stein R. de Borst T.J.R. Hughes Encyclopedia of Computational Mechanics vol. 3 2004 John Wiley & Sons Ltd. 579-607 (Chapter 18)
42. E. Oñate S. Idelsohn A mesh free finite point method for advective-diffusive transport and fluid flow problems Computat. Mech. 21 1998 283-292
43. E. Oñate C. Sacco S. Idelsohn A finite point method for incompressible flow problems Comput. Visualization Sci. 2 2000 67-75
44. S.R. Idelsohn, E. Oñate, F. Del Pin, N. Calvo, Lagrangian formulation: The only way to solve some free-surface fluid mechanics problems, in: H.A. Mang, F.G. Rammerstorfer, J. Eberhardsteiner (Eds.), Fifth World Congress on Computational Mechanics, July 7-12, Viena, Austria, 2002.
45. S.R. Idelsohn E. Oñate F. Del Pin A Lagrangian meshless finite element method applied to fluid-structure interaction problems Comput. Struct. 81 2003 655-671
46. E. Onãte S.R. Idelsohn F. Del Pin R. Aubry The particle finite element method. An overview Int. J. Comput. Methods 1 2 2004 267-307
47. R. Aubry S.R. Idelsohn E. Oñate Particle finite element method in fluid mechanics including thermal convection-diffusion Comput. Struct. 83 17-18 2005 1459-1475
48. S.R. Idelsohn E. Oñate F. Del Pin The particle finite element method: A powerful tool to solve incompressible flows with free-surfaces and breaking waves Int. J. Numer. Methods Engrg. 61 2004 964-989
49. S.R. Idelsohn E. Oñate N. Calvo F. Del Pin The meshless finite element method Int. J. Numer. Methods Engrg. 58 2003 893-912
50. N. Calvo S.R. Idelsohn E. Oñate The extended Delaunay tesselation Engrg. Computat. 20 5/6 2003 583-600
51. S.R. Idelsohn N. Calvo E. Oñate Polyhydrization of an arbitrary 3D point set Comput. Methods Appl. Mech. Engrg. 192 2003 2649-2667
52. R. Codina Pressure stability in fractional step finite element method for incompressible flows J. Comput. Phys. 170 2001 112-140
53. R. Codina O. Soto Approximation of the incompressible Navier-Stokes equations using orthogonal-subscale stabilization and pressure segregation on anisotropic finite element meshes Comput. Methods Appl. Mech. Engrg. 193 15-16 2004 1403-1419
54. T.E. Tezduyar M. Behr J. Liou 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 tests Comput. Methods Appl. Mech. Engrg. 94 1992 339-351
55. G. Chiandusi G. Bugeda E. Oñate A simple method for update of finite element meshes Commun. Numer. Methods Engrg. 16 2000 1-9
56. D.C. Wilcox Turbulence Modeling for CFD 1994 DCW Industries Inc.
57. H. Edelsbrunner E.P. Mucke Three dimensional alpha shapes ACM Trans. Graphics 13 1999 43-72
58. T.J.R. Hughes M. Mallet 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
59. R. Codina A discontinuity-capturing crosswind dissipation for the finite element solution of the convection-diffusion equation Comput. Methods Appl. Mech. Engrg. 110 1993 325-342
60. E. Oñate J. Rojek R.L. Taylor O.C. Zienkiewicz Finite calculus formulation for incompressible solids using linear triangles and tetrahedra Int. J. Numer. Methods Engrg. 59 2004 1473-1500
61. E. Onãte R.L. Taylor O.C. Zienkiewicz J. Rojek A residual correction method based on finite calculus Engrg. Computat. 20 5/6 2003 629-658
62. J.C. Cante, J. Oliver, C. González, Powder forming simulation with the particle finite element method, in: Z.H. Yao, M.W. Yuan, W.X. Zhong (Eds.), Computational Mechanics, CD-Rom Proceedings of the WCCM VI, Beijing, September 5-10, 2004.
63. E. Onãte, J. Arteaga, J. García, R. Flores, Error estimation and mesh adaptivity in incompressible viscous flows using a residual power approach, Comput. Methods Appl. Mech. Engrg., in press, doi:10.1016/j.cma.2004.07.054.
64. Korea Research Institute of Ships and Ocean Engineering (KRISO), Available from: .
65. R. Löhner C. Yang E. Oñate S. Idelsohn An unstructured grid-based parallel free surface solver Appl. Numer. Math. 31 1999 271-293
66. J. García, R. Luco-Salman, M. Salas, M. López-Rodríguez, E. Oñate, An advanced finite element method for fluid-dynamic analysis of America's Cup boat, in: High Performance Yacht Design Conference, Auckland, 4-6, December, 2002.
67. S.R. Idelsohn E. Oñate C. Sacco Finite element solution of the free surface ship-wave problem Int. J. Numer. Methods Engrg. 45 1999 503-508
68. S. Koshizuka Y. Oka Moving particle semi-implicit method for fragmentation of incompressible fluid Nucl. Engrg. Sci. 123 1996 421-434
69. R. Radovitzki M. Ortiz Lagrangian finite element analysis of a Newtonian flows Int. J. Numer. Methods Engrg. 43 1998 607-619
70. Tdyn. A finite element code for fluid-dynamic analysis, COMPASS Ingeniería y Sistemas SA, Available from: , 2005.