Abstract
Two-phase, incompressible miscible flow in prous media is governed by a system of nonlinear partial differential equations. The pressure equation, which is elliptic in appearance, is discretized by a standard five-points difference method. The concentration equation is treated by an implicit finite difference method that applies a form of the method of characteristics to the transport terms. A class of biquadratic interpolation is introduced for the method of characteristics. Convergene rate is proved to be O(Δt+h 2).
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Douglas, J. Jr., Russell, T. F., Numerical method for convection-dominated diffusion problems based on combining the method of characteristics with finite element or finite difference procedures, SIAM J. Numer. Anal., 1982, 19: 871–885.
Douglas, J. Jr., Finite difference methods for two-phase incompressible flow in porous media. SIAM J. Numer. Anal., 1983, 20: 681–696.
Yuan Yirang, Finite diffrence methods for a compressible, miscible displacement in porous media, Math. Numer. Sinica, 1993, 15: 16–28.
Douglas, J. Jr., The numerical solution of miscible displacement in porous media, In: Oden, J.T., ed., Computational Methods in Nonlinear Mechanics, North-Holland, Amsterdam, 1980.
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This work is supported by National Natural Science Foundation of China and the Doctoral Foundation of National Education Ministry.
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Aijie, C. Characteristics difference method for incompressible miscible flow in porous media. Appl. Math. Chin. Univ. 14, 144–152 (1999). https://doi.org/10.1007/s11766-999-0020-3
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DOI: https://doi.org/10.1007/s11766-999-0020-3