Finite difference schemes for incompressible flows in the velocity - impulse density formulation

Journal of Computational Physics

Volumn 130, Issue 1, 1997, Pages 67-76

  Weinan, E ^a   Liu, Jian Guo ^b  

^a NEW YORK UNIVERSITY   (United States)

^b Temple University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

FINITE DIFFERENCE METHOD; INCOMPRESSIBLE FLOW;

FINITE DIFFERENCE SCHEME; ILL POSED; IMPULSE DENSITIES; INVISCID FLOWS; NONLINEAR TERMS; NUMERICAL EVIDENCE; NUMERICAL RESULTS; PRIMITIVE VARIABLES; VARIABLE FORMULATION; VELOCITY IMPULSE;

NUMERICAL METHODS;

EID: 0030637848     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcph.1996.5537     Document Type: Article

References (21)

1. 1. J. B. Bell, P. Collela, and H. G. Glaz, J. Comput. Phys. 85(1989), pp. 257-283.
2. 2. T. Buttke, Velocity methods: Lagrangian numerical methods which preserve the Hamiltonian structure of incompressible fluid flow, in Vortex Flows and Related Numerical Methods, edited by J. T. Beale, G. H. Cottet and S. Huberson (Kluwer, Dordrecht) 1993.
3. 3. T. Buttke and A. Chorin, Turbulence calculation using magnetization variables, Appl. Numer. Math. 12, 47-54 (1993).
4. 4. S. G. Chefranov, The dynamics of point vortex dipoles and spontaneous singularities in three-dimensional turbulent flows, Sov. Phys. JETP 66, 85 (1987).
5. 5. M. Chen, thesis, NYU.
6. 6. A. Chorin, Bull. Amer. Math. Soc. 73, 928 (1967).
7. 7. A. Chorin, Microstructure, renormalization, and more efficient vortex method, preprint, 1995.
8. 8. R. Cortez, in Proceedings of the Second International Workshop on Vortex Flows and Related Numerical Methods, Montreal, August 1995, to appear.
9. 9. W. E and J.-G. Liu, Vorticity boundary condition and related issues for finite difference schemes, J. Comput. Phys. 124, 368 (1996).
10. 10. W. E and J.-G. Liu, preprint, 1996.
11. 11. W. E and C. W. Shu, A numerical resolution study of high order ENO schemes applied to incompressible flows, J. Comput. Phys. 110, No. 1 (1994), 39.
12. 12. U. Ghia, K. N. Ghia, and C. T. Shin, High-re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method, J. Comput. Phys. 48, 387 (1982).
13. 13. J. Kim and P. Moin, J. Comput. Phys. 97, 414 (1991).
14. 14. V. I. Oseledets, On a new way of writing the Navier-Stokes equation. The Hamiltonian formalism, Russ. Math. Surveys 44, 210 (1989).
15. 15. C. M. Rhie and W. L. Chow, AIAA J. 21, 1525 (1983).
16. 16. R. D. Richtmyer and K. W. Morton, Difference Methods for Initial Value Problems, Wiley-Interscience, New York, 1967.
17. 17. P. Roberts, A Hamiltonian theory for weakly interacting vortices, Mathematica 19, 169-179 (1972).
18. 18. R. Schreiber and H. B. Keller, Driven cavity flows by efficient numerical techniques, J. Comput. Phys. 49(1983) 310-333.
19. 19. D. Summers and A. Chorin, in Proceedings of the Second International Workshop on Vortex Flows and Related Numerical Methods, Montreal, August 1995, to appear.
20. 20. R. Temam, Arch. Rat. Mech. Anal. 33, 377 (1969).
21. 21. J. van Kan, SIAM J. Sci. Statist. Comp. 7, 870 (1986).