Least-squares finite element formulations for viscous incompressible and compressible fluid flows

Computer Methods in Applied Mechanics and Engineering

Volumn 195, Issue 19-22, 2006, Pages 2454-2494

  Pontaza, J P ^a   Reddy, J N ^a  

^a Texas A and M University   (United States)

Author keywords

Compressible flow; Incompressible flow; Least squares finite element formulations; Spectral hp methods

Indexed keywords

COMPRESSIBLE FLOW; INCOMPRESSIBLE FLOW; LEAST SQUARES APPROXIMATIONS; MATHEMATICAL MODELS; NAVIER STOKES EQUATIONS; VISCOUS FLOW;

LEAST SQUARES COLLOCATION SOLUTION; LEAST SQUARES FINITE ELEMENT FORMULATIONS;

FINITE ELEMENT METHOD;

COMPRESSIBLE FLOW; FINITE ELEMENT METHOD; INCOMPRESSIBLE FLOW; LEAST SQUARES APPROXIMATIONS; MATHEMATICAL MODELS; NAVIER STOKES EQUATIONS; VISCOUS FLOW;

EID: 33644589019     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2005.05.018     Document Type: Article

References (56)

1. A.K. Aziz R.B. Kellogg A.B. Stephens Least-squares methods for elliptic systems Math. Comput. 44 1985 53-70
2. B.C. Bell K.S. Surana A space-time coupled p-version least-squares finite element formulation for unsteady fluid dynamics problems Int. J. Numer. Methods Engrg. 37 1994 3545-3569
3. B.C. Bell K.S. Surana A space-time coupled p-version least-squares finite element formulation for unsteady two-dimensional Navier-Stokes equations Int. J. Numer. Methods Engrg. 39 1996 2593-2618
4. C. Bernardi Y. Maday A.T. Patera A new nonconforming approach to domain decomposition: The mortar element method H. Brezis J.L. Lions Nonlinear Partial Differential Equations and their Applications 1992 Pitman and Wiley
5. P.B. Bochev Analysis of least-squares finite element methods for the Navier-Stokes equations SIAM J. Numer. Anal. 34 1997 1817-1844
6. P.B. Bochev M.D. Gunzburger Finite element methods of least-squares type SIAM Rev. 40 1998 789-837
7. P.B. Bochev Z. Cai T.A. Manteuffel S.F. McCormick Analysis of velocity-flux first-order system least-squares principles for the Navier-Stokes equations: Part I SIAM J. Numer. Anal. 35 1998 990-1099
8. P.B. Bochev T.A. Manteuffel S.F. McCormick Analysis of velocity-flux least-squares principles for the Navier-Stokes equations: Part II SIAM J. Numer. Anal. 36 1999 1125-1144
9. P. Bolton R.W. Thatcher On mass conservation in least-squares methods J. Comput. Phys. 203 2005 287-304
10. Z. Cai T.A. Manteuffel S.F. McCormick First-order system least-squares for the Stokes equations, with application to linear elasticity SIAM J. Numer. Anal. 33 1997 1727-1741
11. Z. Cai X. Ye A least-squares finite element approximation for the compressible Stokes equations Numer. Methods Partial Differential Eq. 16 2000 62-70
12. Y. Cao M.D. Gunzburger Least-squares finite element approximations to solutions of interface problems SIAM J. Numer. Anal. 35 1998 393-405
13. G.F. Carey J.T. Oden Finite Elements: A Second Course vol. II 1983 Prentice-Hall New Jersey
14. C.L. Chang J.J. Nelson Least-squares finite element method for the Stokes problem with zero residual of mass conservation SIAM J. Numer. Anal. 34 1997 480-489
15. T.F. Chen G.J. Fix Least-squares finite element simulation of transonic flows Appl. Numer. Math. 2 1986 399-408
16. J. Chung G.M. Hulbert A time integration algorithm for structural dynamics with improved numerical dissipation: The generalized α-method J. Appl. Mech. 60 1993 371-375
17. J.M. Deang M.D. Gunzburger Issues related to least-squares finite element methods for the Stokes equations SIAM J. Sci. Comput. 20 1998 878-906
18. W. Dettmer D. Peric An analysis of the time integrator algorithms for the finite element solutions of incompressible Navier-Stokes equations based on a stabilised formulation Comput. Methods Appl. Mech. Engrg. 192 2003 1177-1226
19. E.D. Eason A review of least-squares methods for solving partial differential equations Int. J. Numer. Methods Engrg. 10 1976 1021-1046
20. M.I. Gerritsma M.M.J. Proot Analysis of a discontinuous least-squares spectral element method J. Sci. Comput. 17 2002 297-306
21. U. Ghia K.N. Ghia C.T. Shin High-resolution for incompressible flow using the Navier-Stokes equations and the multigrid method J. Comput. Phys. 48 1982 387-411
22. W. Heinrichs Least-squares spectral collocation for discontinuous and singular perturbation problems J. Comput. Appl. Math. 157 2003 329-345
23. D. Jespersen A least-squares decomposition method for solving elliptic equations Math. Comput. 31 1977 873-880
24. B.N. Jiang C.L. Chang Least-squares finite elements for the Stokes problem Comput. Methods Appl. Mech. Engrg. 78 1990 297-311
25. B.N. Jiang L.A. Povinelli Least-squares finite element method for fluid dynamics Comput. Methods Appl. Mech. Engrg. 81 1990 13-37
26. B.N. Jiang G.F. Carey Least-squares finite element methods for compressible Euler equations Int. J. Numer. Methods Fluids 10 1990 557-568
27. B.N. Jiang A least-squares finite element method for incompressible Navier-Stokes problems Int. J. Numer. Methods Fluids 14 1992 843-859
28. B.N. Jiang The Least-Squares Finite Element Method 1998 Springer-Verlag New York
29. G.E. Karniadakis S.J. Sherwin Spectral/hp Element Methods for CFD 1999 Oxford University Press Oxford
30. S.D. Kim E.J. Lee An analysis of the compressible Stokes equations by first-order system of least-squares finite element method Numer. Methods Partial Differential Eq. 17 2001 689-699
31. L.I.G. Kovasznay Laminar flow behind a two-dimensional grid Proc. Cambridge Philos. Soc. 44 1948 58-62
32. J.P. Laible G.F. Pinder Least-squares collocation solution of differential equations on irregularly shaped domains using orthogonal meshes Numer. Methods Partial Differential Eq. 5 1989 347-361
33. D. Lefebvre J. Peraire K. Morgan Finite element least-squares solution of the Euler equations using linear and quadratic approximations Int. J. Comput. Fluid Dyn. 1 1993 1-23
34. I. Lomtev C.B. Quillen G.E. Karniadakis Spectral/hp methods for viscous compressible flows on unstructured 2D meshes J. Comput. Phys. 144 1998 325-357
35. S. Mittal Finite element computation of unsteady viscous compressible flows Comput. Methods Appl. Mech. Engrg. 157 1998 151-175
36. J. Nordström The use of characteristic boundary conditions for the Navier-Stokes equations Comput. Fluids 24 1995 609-623
37. A. Okajima Strouhal numbers of rectangular cylinders J. Fluid Mech. 123 1982 379-398
38. A.N. Pavlov S.S. Sazhin R.P. Fedorenko M.R. Heikal A conservative finite difference method and its application for the analysis of a transient flow around a square prism Int. J. Numer. Methods Heat Fluid Flow 10 2000 6-46
39. J.P. Pontaza J.N. Reddy Spectral/hp least-squares finite element formulation for the Navier-Stokes equations J. Comput. Phys. 190 2003 523-549
40. J.P. Pontaza J.N. Reddy Space-time coupled spectral/hp least-squares finite element formulation for the incompressible Navier-Stokes equations J. Comput. Phys. 197 2004 418-459
41. J.P. Pontaza X. Diao J.N. Reddy K.S. Surana Least-squares finite element models of two-dimensional compressible flows Finite Elements Anal. Des. 40 2004 629-644
42. M.M.J. Proot M.I. Gerritsma Least-squares spectral elements applied to the Stokes problem J. Comput. Phys. 181 2002 454-477
43. J.N. Reddy Energy Principles and Variational Methods in Applied Mechanics second ed. 2002 John Wiley New York
44. R.L. Sani P.M. Gresho Resume and remarks on the open boundary condition minisymposium Int. J. Numer. Methods Fluids 18 1994 983-1008
45. A. Sohankar C. Norberg L. Davisdon Low-Reynolds-number flow around a square cylinder at incidence: Study of blockage, onset of vortex shedding and outlet boundary condition Int. J. Numer. Methods Fluids 26 1998 39-56
46. K.S. Surana A.R. Ahmadi J.N. Reddy The k-version of finite element method for self-adjoint operators in BVP Int. J. Comput. Engrg. Sci. 3 2002 155-218
47. F. Taghaddosi W.G. Habashi W. Guevremont D. Ait-Ali-Tahia An adaptive least-squares method for the compressible Euler equations Int. J. Numer. Methods Fluids 31 1999 1121-1139
48. L.Q. Tang T.T.H. Tsang A least-squares finite element method for time dependent incompressible flows with thermal convection Int. J. Numer. Methods Fluids 17 1993 271-289
49. L.Q. Tang T. Cheng T.T.H. Tsang Transient solutions for three-dimensional lid-driven cavity flows by a least-squares finite element method Int. J. Numer. Methods Fluids 21 1995 413-432
50. L.Q. Tang T.T.H. Tsang Temporal, spatial and thermal features of 3-D Rayleigh-Benard convection by a least-squares finite element method Comput. Methods Appl. Mech. Engrg. 140 1997 201-219
51. D.J. Tritton Experiments on the flow past a circular cylinder at low Reynolds numbers J. Fluid Mech. 6 1959 547-567
52. C.H.K. Williamson Evolution of a single wake behind a pair of bluff bodies J. Fluid Mech. 159 1985 1-18
53. D. Winterscheidt K.S. Surana p-Version least-squares finite element formulation for two-dimensional incompressible fluid flow Int. J. Numer. Methods Fluids 18 1994 43-69
54. S.T. Yu B.N. Jiang N.S. Liu A div-curl-grad formulation for compressible buoyant flows solved by the least-squares finite element method Comput. Methods Appl. Mech. Engrg. 137 1996 59-88
55. M.M. Zdravkovich Flow Around Circular Cylinders vol. II 2003 Oxford University Press Oxford
56. O.C. Zienkiewicz D.R.J. Owen K.N. Lee Least square-finite element for elasto-static problems. Use of 'reduced' integration Int. J. Numer. Methods Engrg. 8 1974 341-358