An upwinding cell-centered method with piecewise constant velocity over covolumes

Numerical Methods for Partial Differential Equations

Volumn 15, Issue 1, 1999, Pages 49-62

  Chou, So Hsiang ^a   Vassilevski, Panayot S ^b  

^a BOWLING GREEN STATE UNIVERSITY   (United States)

^b BULGARIAN ACADEMY OF SCIENCES   (Bulgaria)

Author keywords

Cell centered method; Covolumes; Finite volume method

Indexed keywords

EID: 0041910100     PISSN: 0749159X     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1098-2426(199901)15:1<49::AID-NUM3>3.0.CO;2-G     Document Type: Article

References (16)

1. J. Roberts and J. Thomas, "Mixed and hybrid methods," in Handbook of Numerical Analysis, Vol. II, P. G. Ciarlet and J. L. Lions, Eds., North-Holland, Amsterdam, 1991.
2. M. Liu, J. Wang, and N. Van, "New error estimates for approximate solutions of convection-diffusion problems by mixed and discontinuous galerkin methods" (1997) preprint.
3. S. H. Chou, "Analysis and convergence of a covolume method for the generalized Stokes problem," Math. Comp. 66, 85-104 (1997).
4. F. H. Harlow and F. E. Welch, "Numerical calculations of time dependent viscous incompressible flow of fluid with a free surface," Phys. Fluids 8, 2181 (1965).
5. R. A. Nicolaides, T. A. Porsching, and C. A. Hall, "Covolume methods in computational fluid dynamics," in Computational Fluid Dynamics Review, M. Hafez and K. Oshma, Eds., John Wiley, 1995, 279-299.
6. Z. Cai, J. E. Jones, S. F. McCormick, and T. F. Russell, "Control-volume mixed finite element methods," Comp. Geosciences, to appear.
7. S. H. Chou and D. Y. Kwak, "Analysis and convergence of a MAC-like scheme for the generalized Stokes problem," Numer. Meth. Partial Diff. Eq. 13, 1-16 (1997).
8. S. H. Chou and D. Y. Kwak, "A covolume method based on rotated bilinears for the generalized Stokes problem," SIAM J. Numer. Anal. 35, 494-507 (1998).
9. S. H. Chou, D. Y. Kwak, and P. Vassilevski, "Mixed covolume methods on rectangular grids for convection dominated problems" (1997) preprint.
10. S. H. Chou, D. Y. Kwak, and P. Vassilevski, "Mixed covolume methods for elliptic problems on triangular grids," SIAM J. Num. Anal, to appear.
11. C. A. Hall, T. A. Forschung, and P. Hu, "Covolume-dual variable method for thermally expandable flow on unstructured triangular grids, Comp. Fluid Dyn. 2, 111-139 (1994).
12. S. H. Chou and D. Y. Kwak, "Mixed covolume methods on rectangular grids for elliptic problems," SIAM J. Numer. Anal., submitted (1996).
13. S. H. Chou and P. Vassilevski, "A general mixed co-volume framework for constructing conservative schemes for elliptic problems" (1997) preprint.
14. H. Roos, M. Stynes, and L. Tobiska, Numerical Methods for Singularly Perturbed Differential Equations: Convection-Diffusion and Flow Problems, Springer-Verlag, New York, 1996.
15. K. Morton, Numerical Solution of Convection-Diffusion Problems, Chapman and Hall, London, 1996.
16. ∞ in covolume methods for elliptic and parabolic problems: A unified approach," Math. Comp. submitted (1996).