Algebraic pressure segregation methods for the incompressible navier-stokes equations

Archives of Computational Methods in Engineering

Volumn 15, Issue 3, 2008, Pages 343-369

  Badia, S ^a,b   Codina, R ^a  

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

^b SANDIA NATIONAL LABORATORIES   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CONTROL NONLINEARITIES; CONTROL THEORY; FACTORIZATION; FLUID DYNAMICS; INCOMPRESSIBLE FLOW; SEGREGATION (METALLOGRAPHY); SUBMARINE PIPELINES; VISCOUS FLOW; VORTEX FLOW;

BLOCK FACTORIZATIONS; HIGHER ORDER SCHEMES; LOOP ALGORITHMS; MONOLITHIC SYSTEMS; NON LINEARITIES; ORIGINAL SYSTEMS; PRECONDITIONERS; PRESSURE CORRECTIONS; VELOCITY CORRECTION METHODS;

NAVIER STOKES EQUATIONS;

EID: 56949097652     PISSN: 11343060     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11831-008-9020-3     Document Type: Article

References (100)

1. F Armero JC Simo 1996 Long-term dissipativity of time-stepping algorithms for an abstract evolution equation with application to MHD and Navier-Stokes equations Comput Methods Appl Mech Eng 131 41 90
2. Arrow K, Hurwicz L, Uzawa H (1958) Studies in nonlinear programming. Stanford University Press, Stanford
3. I Babuška 1971 Error bounds for the finite element method Numer Math 16 322 333
4. Badia S (2006) Stabilized pressure segregation methods and their application to fluid-structure interaction problems. PhD thesis, Escola Tècnica Superior d'Enginyers de Camins, Canals i Ports, Universitat Politècnica de Catalunya, Barcelona
5. S Badia R Codina 2007 Convergence analysis of the FEM approximation of the first order projection method for incompressible flows with and without the inf-sup condition Numer Math 107 4 533 557
6. S Badia R Codina 2007 On some fluid-structure iterative algorithms using pressure segregation methods. Application to aeroelasticity Int J Numer Methods Eng 72 46 71
7. S Badia R Codina 2008 Pressure segregation methods based on a discrete pressure Poisson equation. An algebraic approach Int J Numer Methods Fluids 56 4 351 382
8. GA Baker VA Dougalis A Karakashian 1982 On a higher order accurate fully discrete Galerkin approximation to the Navier-Stokes equations Math Comput 39 339 375
9. JB Bell P Colella HM Glaz 1989 A second-order projection method for the incompressible Navier-Stokes equations J Comput Phys 85 257 283
10. J Blasco R Codina 2001 Space and time error estimates for a first order, pressure stabilized finite element method for the incompressible Navier-Stokes equations Appl Numer Math 38 475 497
11. J Blasco R Codina 2004 Error estimates for an operator splitting method for incompressible flows Appl Numer Math 51 1 17
12. J Blasco R Codina A Huerta 1998 A fractional step method for the incompressible Navier-Stokes equations related to a predictor-multicorrector algorithm Int J Numer Methods Fluids 28 1391 1419
13. JM Boland RA Nicolaides 1983 Stability of finite elements under divergence constraints SIAM J Numer Anal 20 722 731
14. Brenner SC, Scott LR (1994) The mathematical theory of finite element methods. Springer, Berlin
15. F Brezzi 1974 On the existence, uniqueness and approximation of saddle point problems arising from Lagrange multipliers RAIRO Anal Numer 8 129 151
16. F Brezzi KJ Bathe 1990 A discourse on the stability conditions for mixed finite element formulations Comput Methods Appl Mech Eng 82 27 57
17. F Brezzi J Douglas 1988 Stabilized mixed methods for the Stokes problem Numer Math 53 225 235
18. Brezzi F, Fortin M (1991) Mixed and hybrid finite element methods. Springer, Berlin
19. F Brezzi J Rappaz PA Raviart 1981 Finite dimensional approximation of nonlinear problems. Part I: Branches of non-singular solutions Numer Math 36 1 25
20. F Brezzi J Rappaz PA Raviart 1981 Finite dimensional approximation of nonlinear problems. Part II: Limit points Numer Math 37 1 28
21. F Brezzi J Rappaz PA Raviart 1981 Finite dimensional approximation of nonlinear problems. Part III: Simple bifurcation points Numer Math 38 1 30
22. AN Brooks TJR Hughes 1982 Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equation Comput Methods Appl Mech Eng 32 199 259
23. J Cahouet J-P Chabard 1988 Some fast 3D finite element solvers for the generalized Stokes problem Int J Numer Methods Fluids 8 869 895
24. AJ Chorin 1967 A numerical method for solving incompressible viscous problems J Comput Phys 2 12 26
25. Chorin AJ (1967) The numerical solution of the Navier-Stokes equations for an incompressible fluid. AEC Research and Development Report, NYO-1480-82. New York University, New York, 1967
26. AJ Chorin 1968 Numerical solution of the Navier-Stokes equations Math Comput 22 745 762
27. Chorin AJ (1969) On the convergence of discrete approximation to the Navier-Stokes equations. Math Comput, 23
28. Ciarlet PG (1978) The finite element method for elliptic problems. North-Holland, Amsterdam
29. Clay Mathematics Institute (2000) http://www.claymath.org/millenium/. Millennium Problems
30. R Codina 1998 Comparison of some finite element methods for solving the dif fusion-convection-reaction equation Comput Methods Appl Mech Eng 156 185 210
31. R Codina 2000 Stabilization of incompressibility and convection through orthogonal sub-scales in finite element methods Comput Methods Appl Mech Eng 190 1579 1599
32. R Codina 2001 Pressure stability in fractional step finite element methods for incompressible flows J Comput Phys 170 112 140
33. R Codina 2002 Stabilized finite element approximation of transient incompressible flows using orthogonal subscales Comput Methods Appl Mech Eng 191 4295 4321
34. Codina R, Badia S (2004) Second order fractional step schemes for the incompressible Navier-Stokes equations. Inherent pressure stability and pressure stabilization. In: Proceedings of WCCM VI, Beijing, China, 2004
35. R Codina S Badia 2006 On some pressure segregation methods of fractional-step type for the finite element approximation of incompressible flow problems Comput Methods Appl Mech Eng 195 2900 2918
36. R Codina J Blasco 1997 A finite element formulation for the Stokes problem allowing equal velocity-pressure interpolation Comput Methods Appl Mech Eng 143 373 391
37. R Codina J Blasco 2000 Analysis of a pressure-stabilized finite element approximation of the stationary Navier-Stokes equations Numer Math 87 59 81
38. R Codina J Blasco 2002 Analysis of a stabilized finite element approximation of the transient convection-diffusion-reaction equation using orthogonal subscales Comput Vis Sci 4 167 174
39. R Codina A Folch 2004 A stabilized finite element predictor-corrector scheme for the incompressible Navier-Stokes equations using a nodal based implementation Int J Numer Methods Fluids 44 483 503
40. R Codina J Principe O Guasch S Badia 2007 Time dependent subscales in the stabilized finite element approximation of incompressible flow problems Comput Methods Appl Mech Eng 196 24132 2430
41. R Codina O Soto 2004 Approximation of the incompressible Navier-Stokes equations using orthogonal-subscale stabilization and pressure segregation on anisotropic finite element meshes Comput Methods Appl Mech Eng 193 1403 1419
42. de Rham G (1973) Variétés différentiables formes, courants, formes harmoniques. Hermann, Paris
43. W E JG Liu 1995 Projection method I: Convergence and numerical boundary layers SIAM J Numer Anal 32 1017 1057
44. HC Elman 2002 Preconditioners for saddle point problems arising in computational fluid dynamics Appl Numer Math 43 75 89
45. HC Elman VE Howle JN Shadid RS Tuminaro 2003 A parallel block multi-level preconditioner for the 3D incompressible Navier-Stokes equations J Comput Phys 187 504 523
46. HC Elman DJ Silvester AJ Wathen 2002 Block preconditioners for the discrete incompressible Navier-Stokes equations Int J Numer Methods Fluids 40 333 344
47. Ern A, Guermond JL (2004) Theory and practice of finite elements. Springer, Berlin
48. L Franca R Stenberg 1991 Error analysis of some Galerkin least-squares methods for the elasticity equations SIAM J Numer Anal 28 1680 1697
49. I Fried DS Malkus 1975 Finite element mass matrix lumping by numerical integration with no convergence rate loss Int J Solids Struct 11 461 466
50. Gervasio P (2006) Convergence analysis of high order algebraic fractional step schemes for time-dependent Stokes equations. Technical report, Quaderno del Seminario Matematico di Brescia, 2006
51. P Gervasio F Saleri 2006 Algebraic fractional-step schemes for time-dependent incompressible Navier-Stokes equations J Sci Comput 27 1-3 257 269
52. P Gervasio F Saleri A Veneziani 2006 Algebraic fractional-step schemes with spectral methods for the incompressible Navier-Stokes equations J Comput Phys 214 1 347 365
53. Girault V, Raviart PA (1986) Finite element methods for Navier-Stokes equations. Springer, Berlin
54. Gresho PM, Sani RL (2000) Incompressible flow and the finite element method. Wiley, New York
55. PM Gresho 1990 On the theory of semi-implicit projection methods for viscous incompressible flow and its implementation via a finite element method that also introduces a nearly consistent mass matrix. Part I: Theory Int J Numer Methods Fluids 11 587 620
56. 1 for transient viscous incompressible flow Int J Numer Methods Fluids 21 837 856
57. JL Guermond 1994 Remarques sur les méthodes de projection pour l'approximation des équations de Navier-Stokes Numer Math 67 465 473
58. JL Guermond P Minev J Shen 2006 An overview of projection methods for incompressible flows Comput Methods Appl Mech Eng 195 6011 6045
59. JL Guermond L Quartapelle 1998 On stability and convergence of projection methods based on pressure Poisson equation Int J Numer Methods Fluids 26 1039 1053
60. JL Guermond L Quartapelle 1998 On the approximation of the unsteady Navier-Stokes equations by finite element projection methods Numer Math 80 207 238
61. JL Guermond J Shen 2003 A new class of truly consistent splitting schemes for incompressible flows J Comput Phys 192 262 276
62. JL Guermond J Shen 2003 Velocity-correction projection methods for incompressible flows SIAM J Numer Anal 41 112 134
63. JL Guermond J Shen 2004 On the error estimates for the rotational pressure-correction projection methods Math Comput 73 1719 1737
64. JG Heywood R Rannacher 1982 Finite element approximation of the nonstationary Navier-Stokes problem. I: Regularity of solutions and second-order error estimates for spatial discretization SIAM J Numer Anal 19 275 311
65. E Hinton T Rock OC Zienkiewicz 1976 A note on mass lumping and related processes in the finite element method Earthquake Eng Struct Dyn 4 245 249
66. TJR Hughes 1995 Multiscale phenomena: Green's function, the Dirichlet-to-Neumann formulation, subgrid scale models, bubbles and the origins of stabilized formulations Comput Methods Appl Mech Eng 127 387 401
67. TJR Hughes LP Franca GM Hulbert 1987 A new finite element formulation for computational fluid dynamics: VII. The Stokes problem with various well-posed boundary conditions: symmetric formulations that converge for all velocity/pressure spaces Comput Methods Appl Mech Eng 65 85 96
68. TJR Hughes LP Franca GM Hulbert 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 73 173 189
69. Hundsdorfer W, Verwer JG (2003) Numerical solution of time-dependent advection-diffusion-reaction equations. Springer, Berlin
70. GE Karniadakis M Israeli SE Orszag 1991 High order splitting methods for the incompressible Navier-Stokes equations J Comput Phys 59 414 443
71. J Kim P Moin 1985 Application of the fractional step method to incompressible Navier-Stokes equations J Comput Phys 59 308 323
72. Ladyzhenskaya O (1969) The mathematical theory of viscous incompressible flow. Gordon and Breach, New York
73. J Leray 1934 Essai sur les mouvements d'un liquide visqueux emplissant l'espace Acta Math 63 193 248
74. D Loghin AJ Wathen 2002 Schur complement preconditioners for the Navier-Stokes equations Int J Numer Methods Fluids 40 403 412
75. Oden JT, Demkowicz LZ (1996) Applied functional analysis. CRC Press, Boca Raton
76. SA Orszag M Israeli M Deville 1986 Boundary conditions for incompressible flows J Sci Comput 1 75 111
77. JB Perot 1993 An analysis of the fractional step method J Comput Phys 108 51 58
78. Prohl A (1997) Projection and quasi-compressibility methods for solving the incompressible Navier-Stokes equations. Teubner, Stuttgart
79. A Quarteroni G Sacchi Landriani A Valli 1991 Coupling viscous and inviscid Stokes equations via a domain decomposition method for finite elements Numer Math 59 831 859
80. A Quarteroni F Saleri A Veneziani 1999 Analysis of the Yosida method for the incompressible Navier-Stokes equations J Math Pures Appl 78 473 503
81. A Quarteroni F Saleri A Veneziani 2000 Factorization methods for the numerical approximation of Navier-Stokes equations Comput Methods Appl Mech Eng 188 505 526
82. Rannacher R (1992) On Chorin's projection method for incompressible Navier-Stokes equations. Lecture notes in mathematics, vol 1530. Springer, Berlin, pp 167-183
83. Saad Y (1996) Iterative methods for sparse linear systems. PWS-Kent, Boston
84. F Saleri A Veneziani 2005 Pressure correction algebraic splitting methods for the incompressible Navier-Stokes equations SIAM J Numer Anal 43 1 174 194
85. J Shen 1992 On error estimates for some higher order projection and penalty-projection methods for Navier-Stokes equations Numer Math 62 49 73
86. J Shen 1992 On error estimates of projection methods for Navier-Stokes equations: first order schemes SIAM J Numer Anal 29 57 77
87. J Shen 1993 A remark on the projection-3 method Int J Numer Methods Fluids 16 249 253
88. J Shen 1994 Remarks on the pressure error estimates for the projection methods Numer Math 67 513 520
89. J Shen 1996 On error estimates of the projection methods for the Navier-Stokes equations: second-order schemes Math Comput 65 1039 1065
90. JC Simo F Armero 1994 Unconditional stability and long term behavior of transient algorithms for the incompressible Navier-Stokes equations Comput Methods Appl Mech Eng 111 111 154
91. Strang G, Fix J (1973) An analysis of the finite element method. Prentice Hall, Englewood Cliffs
92. R Temam 1968 Sur la stabilité et la convergence de la méthode des pas fractionaires Ann Math Pures Appl LXXIV 191 380
93. R Temam 1968 Une méthode d'approximations de la solution des equations de Navier-Stokes Bull Soc Math Fr 98 115 152
94. R Temam 1969 Sur l'approximation de la solution des équations de Navier-Stokes par la méthode des pas fractionaires (I) Arch Ration Mech Anal 32 135 153
95. R Temam 1969 Sur l'approximation de la solution des équations de Navier-Stokes par la méthode des pas fractionaires (II) Arch Ration Mech Anal 33 377 385
96. Temam R (1984) Navier-Stokes equations. North-Holland, Amsterdam
97. R Temam 1991 Remark on the pressure boundary condition for the projection method Theor Comput Fluid Dyn 3 181 184
98. LJP Timmermans PD Minev FN Van de Vosse 1996 An approximate projection scheme for incompressible flow using spectral elements Int J Numer Methods Fluids 22 673 688
99. Turek S (1999) Efficient solvers for incompressible flow problems. Lecture notes in computational science and engineering. Springer, Berlin
100. J van Kan 1986 A second-order accurate pressure correction scheme for viscous incompressible flow SIAM J Sci Stat Comput 7 870 891