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Front tracking for two‐phase flow in reservoir simulation by adaptive mesh
Author(s) -
Saad Mazen,
Zhang Huilong
Publication year - 1997
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(199711)13:6<673::aid-num5>3.0.co;2-o
Subject(s) - partial differential equation , finite volume method , mathematics , grid , upwind scheme , hyperbolic partial differential equation , elliptic partial differential equation , flow (mathematics) , adaptive mesh refinement , mathematical analysis , geometry , computational science , mechanics , physics , discretization
In this article, an algorithm for the numerical approximation of two‐phase flow in porous media by adaptive mesh is presented. A convergent and conservative finite volume scheme for an elliptic equation is proposed, together with the finite difference schemes, upwind and MUSCL, for a hyperbolic equation on grids with local refinement. Hence, an IMPES method is applied in an adaptive composite grid to track the front of a moving solution. An object‐oriented programmation technique is used. The computational results for different examples illustrate the efficiency of the proposed algorithm. © 1997 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 13: 673–697, 1997