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Minimization of grid orientation effects in simulation of oil recovery processes through use of an unsplit higher order scheme
Author(s) -
Bourgeat Alain,
Koebbe Joe
Publication year - 1996
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(199603)12:2<161::aid-num2>3.0.co;2-o
Subject(s) - grid , orientation (vector space) , mathematics , operator (biology) , dispersion (optics) , mathematical optimization , scheme (mathematics) , conservation law , displacement (psychology) , minification , finite difference , computer simulation , geometry , mathematical analysis , psychology , biochemistry , chemistry , physics , statistics , repressor , transcription factor , optics , psychotherapist , gene
We present an unsplit second‐order finite difference algorithm for hyperbolic conservation laws in several variables. Although the method can be directly implemented for general hyperbolic systems, we focus in this article on reducing grid orientation effects in porous media flow. In particular, we consider miscible and immiscible displacement processes. Our main concern is to develop a scheme that can easily be implemented into existing standard finite‐difference‐based reservoir simulators as an option to be used if grid orientation effects occur. The principle of the scheme is to build a higher order scheme to reduce numerical dispersion and that does not split the spatial operator to reduce the effect of the grid orientation. Numerical results are presented, which show that the method presented here reduces the effect of the numerical dispersion to a level that minimizes the grid orientation effects in a computationally efficient manner. © 1996 John Wiley & Sons, Inc.