Systematic approach to mathematical modeling of filtration processes in multiply-connected curvilinear LEF-layers
DOI:
https://doi.org/10.20535/SRIT.2308-8893.2016.2.06Keywords:
mathematical modeling, filtration processes, multiply-connected domains, summary representations methods, numerical methods of complex analysis, domain decomposition, LEF-layerAbstract
The constructive systematic approach to mathematical modeling of filtration processes for the three- and four-connected curvilinear LEF-domains bounded equipotential lines was developed on the basis of synthesis of methods of complex analysis and numerical-analytical methods of summary representations. The problem of ambiguity of constructing the domain of the complex quasi-potential for multiply-connected LEF-domains that model the interaction of injection and production wells in oil and gas reservoirs was solved. The classification of cases of the flow forming, that allows to unify the formulation of problems of inversion of quasiconformal mappings and their difference analogues. The algorithm for solving the problem was constructed that auto-matically constructs the dynamic grids, finds unknown separation lines and points of "suspension" of the flow, calculates the total flow, and so on. The numerical calculations for one of the variants of the flow formation are presented.References
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