Spectral/hp least-squares finite element formulation for the Navier-Stokes equations

Journal of Computational Physics

Volumn 190, Issue 2, 2003, Pages 523-549

  Pontaza, J P ^a   Reddy, J N ^a  

^a Texas AandM University   (United States)

Author keywords

hp methods; Incompressible flow; Least squares; Low speed compressible flow; Spectral methods

Indexed keywords

COMPRESSIBLE FLOW; CONJUGATE GRADIENT METHOD; FINITE ELEMENT METHOD; INCOMPRESSIBLE FLOW; LEAST SQUARES APPROXIMATIONS; LINEAR SYSTEMS; NEWTON-RAPHSON METHOD; NUMERICAL METHODS; VISCOUS FLOW;

FINITE ELEMENT MODELLING (FEM); HP METHOD; LEAST SQUARE; LEAST-SQUARES FINITE ELEMENTS; LOW SPEED; LOW-SPEED COMPRESSIBLE FLOW; NAVIER-STOKES EQUATION; NUMERICAL SOLUTION; SPECTRAL METHODS; SPECTRAL/HP;

NAVIER STOKES EQUATIONS;

EID: 0141850310     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0021-9991(03)00296-1     Document Type: Article

References (33)

1. G.E. Karniadakis, S.J. Sherwin, Spectral/hp Element Methods forCFD, Oxford University Press, Oxford, 1999.
2. J.N. Reddy, Energy Principles and Variational Methods in Applied Mechanics, second ed., Wiley, New York, 2002.
3. V. Girault, P. Raviart, Finite Element Methods for Navier-Stokes Equations, Springer, Berlin, 1986.
4. F. Brezzi, J. Douglas, Stabilized mixed methods for the Stokes problem, Numer. Math. 53 (1988) 225.
5. L. Franca, R. Stenberg, Error analysis of some Galerkin least-squares methods for the elasticity equations, SIAM J. Numer. Anal. 28 (1991) 1680.
6. B.N. Jiang, The Least-Squares Finite Element Method, Springer, Berlin, 1998.
7. P.B. Bochev, M.D. Gunzburger, Finite element methods of least-squares type, SIAM Rev. 40 (1998) 789.
8. S. Agmon, A. Douglis, L. Nirenberg, Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions II, Commun. Pure Appl. Math. 17 (1964) 35.
9. Z. Cai, T.A. Manteuffel, S.F. McCormick, First-order system least-squares for the Stokes equations, with applications to linear elasticity, SIAM J. Numer. Anal. 34 (1997) 1727.
10. P.B. Bochev, Analysis of least-squares finite element methods for the Navier-Stokes equations, SIAM J. Numer. Anal. 34 (1997) 1817.
11. B.N. Jiang, A least-squares finite element method for incompressible Navier-Stokes problems, Int. J. Numer. Methods Fluids 14 (1992) 843.
12. L.Q. Tang, 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. Eng. 140 (1997) 201.
13. P.B. Bochev, Z. Cai, T.A. Manteuffel, S.F. McCormick, Analysis of velocity-flux least-squares principles for the Navier-Stokes equations, Part I, SIAM J. Numer. Anal. 35 (1998) 990.
14. B.N. Jiang, V. Sonnad, Least-squares solution of incompressible Navier-Stokes equations with the p-version of finite elements, Comput. Mech. 15 (1994) 129.
15. 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.
16. M. Bagheri, K.S. Surana, p-Version least-squares finite element formulation for steady-state two-dimensional turbulent flows using the k-E model of turbulence, Commun. Numer. Meth. Eng. 16 (2000) 97.
17. T.C. Warburton, S.J. Sherwin, G.E. Karniadakis, Basis functions for triangular and quadrilateral high-order elements, SIAM J. Sci. Comput. 20 (1999) 1671.
18. D.K. Gartling, A test problem for outflow boundary conditions - flow over a backward-facing step, Int. J. Numer. Methods Fluids 11 (1990) 953.
19. A.S. Grove, F.H. Shair, E.E. Petersen, A. Acrivos, An experimental investigation of the steady separated flow past a circular cylinder, J. Fluid Mech. 19 (1964) 60.
20. B.N. Jiang, T.L. Lin, L.A. Povinelli, Large-scale computation of incompressible viscous flow by least-squares finite element method, Comput. Methods Appl. Mech. Eng. 114 (1994) 213.
21. S.T. Yu, B.N. Jiang, J. Wu, N.S. Liu, A div-curl grad formulation for compressible buoyant flows solved by the least-squares finite element method, Comput. Methods Appl. Mech. Eng. 137 (1996) 59.
22. J.N. Reddy, An Introduction to the Finite Element Method, second ed., McGraw-Hill, New York, 1993.
23. J.N. Reddy, An Introduction to Nonlinear Finite Element Analysis, Oxford University Press (2003) (in press).
24. R.L. Sani, P.M. Gresho, Resume and remarks on the open boundary condition minisymposium, Int. J. Numer. Methods Fluids 18 (1994) 983.
25. L.S.G. Kovasznay, Laminar flow behind a two-dimensional grid, Proc. Camb. Phil. Soc. 44 (1948) 58.
26. M.M.J. Proot, M.I. Gerrtisma, Least-squares spectral elements applied to the Stokes problem, J. Comput. Phys. 181 (2002) 454.
27. Y. Saad, Iterative Methods for Sparse Linear Systems, PWS, 1996.
28. D.J. Tritton, Experiments on the flow past a circular cylinder at low Reynolds numbers, J. Fluid Mech. 6 (1959) 547.
29. S.C.R. Dennis, G.Z. Chang, Numerical solutions for steady flow past a circular cylinder at Reynolds numbers up to 100, J. Fluid Mech. 42 (1970) 471.
30. M. Kawaguti, P. Jain, Numerical study of a viscous fluid past a circular cylinder, J. Phys. Soc. Jpn. 21 (1966) 2055.
31. J.N. Reddy, Penalty-finite-element analysis of 3-D Navier-Stokes equations, Comput. Methods Appl. Mech. Eng. 35 (1982) 87.
32. F.S. Sherman, Viscous Flow, McGraw-Hill, New York, 1990.
33. 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. (accepted for publication).