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Finite difference schemes for two-dimensional miscible displacement flow in porous media on composite triangular grids. (English) Zbl 1155.65371
Summary: Considering two-dimensional miscible displacement flow in porous media, the local grid refinement method of a coupled system on triangular cell-centered grids with local refinement in space is studied. Based on the balance equation, finite difference schemes of the coupled equations on composite grids are constructed. Studying their stability and convergence properties, the error estimate in the energy norm is obtained. Finally, a numerical example is given.
MSC:
65M06Finite difference methods (IVP of PDE)
References:
[1]Yirang, Yuan: Some new progress in the fileds of computational petroleum geology and others, Chinese J. Comput. phys. 20, No. 4, 283-290 (2003)
[2]O.A. Pedrosa Jr., Use of hybrid grid in reservoir simulation. Paper SPE 13507 Presented at the English SPE Symposium on Reservoir Simulation, Dallas, Texas, Feb. 10–13, 1985
[3]Ewing, R. E.; Lazarov, R. D.; Vassilevski, P. S.: Local refinement techniques for elliptic problems on cell-centered grids, I: Error analysis, Math. comp. 56, No. 194, 437-462 (1991) · Zbl 0724.65093 · doi:10.2307/2008390
[4]Ewing, R. E.; Lazarov, R. D.; Vassilevski, P. S.: Local refinement techniques for elliptic problems on cell-centered grids, II: Optimal order two-grid iterative methods, Numer. linear algebra appl. 1, No. 4, 337-368 (1994) · Zbl 0840.65124 · doi:10.1002/nla.1680010403
[5]Ewing, R. E.; Lazarov, R. D.; Vassilevski, P. S.: Local refinement techniques for elliptic problems on cell-centered grids, III: Algebraic multilevel BEPS preconditioners, Numer. math. 59, 431-452 (1991) · Zbl 0726.65137 · doi:10.1007/BF01385790
[6]Lazarov, R. D.; Mishev, I. D.; Vassilevski, P. S.: Finite volume methods with local refinement for convection–diffusion problems, Computing 53, 33-57 (1994) · Zbl 0807.65113 · doi:10.1007/BF02262107
[7]Vassilevski, P. S.; Petrova, S. I.; Lazarov, R. D.: Finite difference schemes on triangular cell-centered grids with local refinement, SIAM J. Sci. stat. Comput. 13, No. 6, 1287-1313 (1992) · Zbl 0813.65115 · doi:10.1137/0913073
[8]Cai, Z. Q.; Mccormick, S. F.: On the accuracy of the finite volume element method for diffusion equations on composite grids, SIAM J. Numer. anal. 27, 636-655 (1990) · Zbl 0707.65073 · doi:10.1137/0727039
[9]Ewing, R. E.; Lazarov, R. D.; Vassilevski, P. S.: Finite difference schemes on grids with local refinement in time and space for parabolic problems, I. Derivation, stability, and error analysis, Computing 45, 193-215 (1990) · Zbl 0721.65047 · doi:10.1007/BF02250633
[10]Ewing, R. E.; Lazarov, R. D.; Vassilevski, P. S.: Finite difference schemes on grids with local refinement in time and space for parabolic problems, II. Optimal order two-grid iterative methods, Lecture notes in fluid mechanics 31, 70-93 (1991) · Zbl 0829.65112
[11]Liu, Baodong; Cheng, Aijie; Lu, Tongchao: The dynamic mixed finite element methods for incompressible miscible displacement in porous media, J. systems sci. Math. sci. 25, 118-128 (2005) · Zbl 1078.65085
[12]Liu, Wei; Yuan, Yirang: A finite difference scheme for three-dimensional semiconductor device on grids with local refinement in time and space, Math. numer. Sin. 28, No. 2, 175-188 (2006)
[13]Jr., Jim Douglas: Finite difference methods for incompressible flow in porous media, SIAM J. Numer. anal. 20, No. 4, 681-696 (1983) · Zbl 0519.76107 · doi:10.1137/0720046