A pure-compact scheme for the streamfunction formulation of Navier-Stokes equations

Journal of Computational Physics

Volumn 205, Issue 2, 2005, Pages 640-664

  Ben Artzi, Matania ^a   Croisille, Jean Pierre ^b   Fishelov, Dalia ^c,d   Trachtenberg, Shlomo ^e  

^a HEBREW UNIVERSITY OF JERUSALEM   (Israel)

^b UNIVERSITÉ DE LORRAINE   (France)

^c AFEKA TEL AVIV ACADEMIC COLLEGE OF ENGINEERING   (Israel)

^d TEL AVIV UNIVERSITY   (Israel)

^e HEBREW UNIVERSITY   (Israel)

Author keywords

Asymptotic behavior; Compact schemes; Driven cavity; Navier Stokes equations; Numerical algorithm; Streamfunction formulation; Symmetry breaking; Vorticity

Indexed keywords

REYNOLDS NUMBER; VISCOUS FLOW; VORTICITY;

ASYMPTOTIC BEHAVIOUR; COMPACT SCHEMES; DRIVEN CAVITY; INCOMPRESSIBLE (NAVIER )STOKES EQUATION; NAVIER-STOKES EQUATION; NUMERICAL ALGORITHMS; STREAMFUNCTION FORMULATION; STREAMFUNCTIONS; SYMMETRY BREAKINGS; TWO-DIMENSIONAL;

NAVIER STOKES EQUATIONS;

EID: 17144404238     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jcp.2004.11.024     Document Type: Article

References (22)

1. I. Altas J. Dym M.M. Gupta R.P. Manohar Mutigrid solution of automatically generated high-order discretizations for the biharmonic equation SIAM J. Sci. Comput. 19 1998 1575-1585
2. M. Ben-Artzi, Vorticity dynamics in planar domains, in preparation
3. M. Ben-Artzi D. Fishelov S. Trachtenberg Vorticity dynamics and numerical resolution of Navier-Stokes equations Math. Model. Numer. Anal. 35 2 2001 313-330
4. D. Calhoun A cartesian grid method for solving the two-dimensional streamfunction-vorticity equations in irregular regions J. Comp. Phys. 176 2002 231-275
5. A.J. Chorin Numerical solution of the Navier-Stokes equations Math. Comp. 22 1968 745-762
6. G.-H. Cottet P.D. Koumoutsakos Vortex Methods. Theory and Practice 2000 Cambridge University Press
7. W. E, J.-G. Liu, Essentially compact schemes for unsteady viscous incompressible flows, J. Comp. Phys. 126 (1996) 122-138
8. W.E, J.-G. Liu, Vorticity boundary condition and related issues for finite difference scheme, J. Comp. Phys. 124 (1996) 368-382
9. D. Fishelov M. Ben-Artzi J.-P. Croisille A compact scheme for the stream-function formulation of Navier-Stokes equations Notes on Computer Science (Springer-Verlag) 2667 2003 809-817
10. U. Ghia K.N. Ghia C.T. Shin High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method J. Comp. Phys. 48 1982 387-411
11. P.M. Gresho Incompressible fluid dynamics: Some fundamental formulation issues Annu. Rev. Fluid Mech. 23 1991 413-453
12. R. Kupferman A central-difference scheme for a pure streamfunction formulation of incompressible viscous flow SIAM J. Sci. Comput. 23 1 2001 1-18
13. H. Lamb Hydrodynamics 6th ed. 1932 Dover
14. Ming Li Tao Tang A compact fourth-order finite difference scheme for unsteady viscous incompressible flows J. Sci. Comput. 16 1 2001 29-45
15. Zhilin Li Cheng Wang A fast finite difference method for solving Navier-Stokes equations in irregular domains Comm. Math. Sci. 1 1 2003 180-196
16. J.L. Lions E. Magenes Non-Homogeneous Boundary Value Problems and Applications I 1972 Springer-Verlag Berlin
17. T.W. Pan R. Glowinski A projection/wave-like equation method for the numerical simulation of incompressible viscous fluid flow modeled by the Navier-Stokes equations Comput. Fluid Dynamics 9 2000
18. L. Quartapelle Numerical Solution of the Incompressible Navier-Stokes Equations 1993 Birkhauser Verlag
19. J. Shen Hopf bifurcation of the unsteady regularized driven cavity J. Comp. Phys. 95 1991 228-245
20. J.W. Stephenson Single cell discretizations of order two and four for biharmonic problems J. Comp. Phys. 55 1984 65-80
21. R. Temam Navier-Stokes Equations 2001 AMS Edition
22. T.E. Tezduyar J. Liou D.K. Ganjoo M. Behr Solution techniques for the vorticity-streamfunction formulation of the two-dimensional unsteady incompressible flows Int. J. Numer. Meth. Fluids 11 1990 515-539