, Volume 187, Issue 5, pp 596-605
Date: 18 Nov 2012

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.

Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 54, No. 4, pp. 52–58, October–December, 2011.