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Finite element method for two‐phase immiscible flow
Author(s) -
Sun Wen Tao,
Zhang Huai Yu
Publication year - 1999
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/(sici)1098-2426(199907)15:4<407::aid-num1>3.0.co;2-w
Subject(s) - finite element method , mathematics , mixed finite element method , extended finite element method , hp fem , smoothed finite element method , partial differential equation , mathematical analysis , parallelizable manifold , computation , upwind scheme , flow (mathematics) , compressibility , partial derivative , finite element limit analysis , boundary knot method , geometry , mechanics , discretization , physics , algorithm , boundary element method , thermodynamics
An explicit finite element method for numerically solving the two‐phase, immiscible, incompressible flow in a porous medium in two space dimensions is analyzed. The method is based on the use of a mixed finite element method for the approximation of the velocity and pressure a discontinuous upwinding finite element method for the approximation of the saturation. The mixed method gives an approximate velocity field in the precise form needed by the discontinuous method, which is trivially conservative and fully parallelizable in computation. It is proven that it converges to the exact solution. © 1999 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 15: 407–416, 1999