期刊
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
卷 191, 期 46, 页码 5265-5286出版社
ELSEVIER SCIENCE SA
DOI: 10.1016/S0045-7825(02)00458-9
关键词
finite volume method; degenerate parabolic equation; nonlinear convection-diffusion; porous media
This paper develops discretizations using the finite volume method for a nonlinear, degenerate, convection-diffusion equation in multiple dimensions on unstructured grids. We will derive three families of numerical schemes. They are classified as explicit, implicit, and semi-implicit. A Godunov scheme is used for the convection term. It is shown that these finite volume schemes (FVS) satisfy a discrete maximum principle. We prove the convergence of these FVS. This is done by means of a priori estimates in L-infinity and weak B V estimates under appropriate CFL conditions. Numerical results for oil recovery simulation are presented. (C) 2002 Elsevier Science B.V. All rights reserved.
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