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The upwind finite difference fractional steps methods for two‐phase compressible flow in porous media
Author(s) -
Yuan Yirang
Publication year - 2003
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/num.10036
Subject(s) - mathematics , upwind scheme , finite difference , compressibility , finite difference method , porous medium , compressible flow , fractional calculus , mathematical analysis , calculus (dental) , porosity , mechanics , medicine , physics , geotechnical engineering , dentistry , discretization , engineering
The upwind finite difference fractional steps methods are put forward for the two‐phase compressible displacement problem. Some techniques, such as calculus of variations, multiplicative commutation rule of difference operators, decomposition of high‐order difference operators, and prior estimates, are adopted. Optimal order estimates in L 2 norm are derived to determine the error in the approximate solution. This method has already been applied to the numerical simulation of seawater intrusion and migration‐accumulation of oil resources. © 2002 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 19: 67–88, 2003