A spatial generalization of the method of conformal mappings for the solution of model boundary-value filtration problems
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We propose a mathematical model for the calculation of the ideal flow in a curvilinear parallelepiped bounded by the stream surfaces and the equipotential ones. We suggest the system of second-order partial differential equations, which relates the potential and the stream functions spatially complexconjugate to it. On this basis, we formulate the problem of finding the spatial conformal mapping of a curvilinear parallelepiped on a rectangular parallelepiped and the corresponding inverse problem (of finding the inverse conformal mapping). An algorithm of solution of the problem is constructed, and the numerical calculations are carried out.
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- A spatial generalization of the method of conformal mappings for the solution of model boundary-value filtration problems
Journal of Mathematical Sciences
Volume 187, Issue 5 , pp 596-605
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