A new paradigm for solving Navier-Stokes equations: Streamfunction-velocity formulation

Journal of Computational Physics

Volumn 207, Issue 1, 2005, Pages 52-68

  Gupta, Murli M ^a   Kalita, Jiten C ^b  

^a GEORGE WASHINGTON UNIVERSITY   (United States)

^b INDIAN INSTITUTE OF TECHNOLOGY GUWAHATI   (India)

Author keywords

Biharmonic equation; Compact approximations; Finite differences; High accuracy; Navier Stokes equations; Streamfunction velocity formulation

Indexed keywords

ASPECT RATIO; EQUATIONS OF STATE; GRADIENT METHODS; NUMERICAL METHODS; PROBLEM SOLVING; VISCOUS FLOW; VORTICITY;

BIHARMONIC EQUATIONS; COMPACT APPROXIMATION; FINITE DIFFERENCE; FLUID FLOW PROBLEMS; HIGH-ACCURACY; INCOMPRESSIBLE FLUID FLOW; NAVIER-STOKES EQUATION; STEADY STATE NAVIER-STOKES EQUATIONS; STREAMFUNCTION-VELOCITY FORMULATION; TWO-DIMENSIONAL;

NAVIER STOKES EQUATIONS;

EID: 18344385504     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jcp.2005.01.002     Document Type: Article

References (20)

1. I. Altas J. Dym M.M. Gupta R. Manohar Multigrid solution of automatically generated high-order discretizations for the biharmonic equation SIAM J. Sci. Comput. 19 1998 1575-1585
2. I. Altas J. Erhel M.M. Gupta High accuracy solution of three-dimensional biharmonic equations Numer. Algorithm 29 2002 1-19
3. E. Barragy G.F. Carey Streamfunction-vorticity driven cavity solution using p finite elements Comp. Fluid 26 1997 453-468
4. O. Botella R. Peyret Benchmark spectral results on the lid-driven cavity flow Comp. Fluid 27 1998 421-433
5. C.-H. Bruneau C. Jouron An efficient scheme for solving steady incompressible Navier-Stokes equations J. Comput. Phys. 89 1990 389-413
6. U. Ghia K.N. Ghia C.T. Shin High Re-solution for incompressible Navier-Stokes equation and a multigrid method J. Comput. Phys. 48 1982 387-411
7. M.M. Gupta Discretization error estimates for certain splitting procedures for solving first biharmonic boundary value problems SIAM J. Numer. Anal. 12 1975 364-377
8. M.M. Gupta L.W. Ehrlich Some difference schemes for the biharmonic equation SIAM J. Numer. Anal. 12 1975 773-790
9. M.M. Gupta R. Manohar Direct solution of biharmonic equation using noncoupled approach J. Comput. Phys. 33 1979 236-248
10. S. Hou Q. Zou S. Chen G. Doolen A. Cogley Simulation of cavity flows by the lattice Boltzmann method J. Comput. Phys. 118 1995 329-347
11. C.T. Kelley Iterative Methods for Linear and Nonlinear Equations 1995 SIAM Publications Philadelphia
12. J. Kim P. Moin Application of fractional step method to incompressible Navier-Stokes equation J. Comput. Phys. 59 1985 308-323
13. Y. Kwon R. Manohar J.W. Stephenson Single cell fourth order methods for the biharmonic equation Congres. Numerantium 34 1982 475-482
14. G. Meurant Computer Solution of Large Linear Systems 1999 North-Holland Amsterdam
15. Y. Saad Iterative Methods for Sparse Linear Systems 1996 PWS Publishing Company
16. R. Schreiber H.B. Keller Driven cavity flows by efficient numerical techniques J. Comput. Phys. 49 1983 310-333
17. G.L.G. Sleijpen H.A. van der Vorst Hybrid biconjugate methods for CFD problems in: M. Hafez K. Oshima (Eds.) Computational Fluid Dynamics Review 1995 457-476
18. J.W. Stephenson Single cell discretizations of order two and four for biharmonic problems J. Comput. Phys. 55 1984 65-80
19. H. van Der Vorst BiCGSTAB: A fast and smoothly converging variant of BiCG for the solution of nonsymmetric linear systems SIAM J. Sci. Comput. 13 1992 631-644
20. S.P. Vanka Block-implicit multigrid solution of Navier-Stokes equations in primitive variables J. Comput. Phys. 65 1986 138-158