IDENTIFICATION OF SEPARATION CURVES OF STRONGLY CONTRASTING ENVIRONMENTS USING COMPLEX ANALYSIS METHODS

Abstract

When modeling mass transfer processes (for example, filtration) in porous media, there may be cases of the existence of highly permeable layers, which are separated from the corresponding studied parts by some curves that must be found (identified) in the process of solving the problem. When constructing a mathematical model of the corresponding physical process, we will consider a highly permeable medium as "ideally (theoretically infinitely) permeable." In this case, the desired curve can be considered an equipotential line. This work considers the stationary process of fluid movement in a homogeneous horizontal layer of infinitely large dimensions - a soil massif, which is limited by infinite sections of curves, in particular by the desired curve of theoretical water resistance and the horizontal axis, on which the local speed of movement is known. On the basis of the methods of conformal reflections and total images, an approach to the identification of the curve of the separation of media is proposed. The constructed algorithm is modified for solving nonlinear inverse boundary value problems on quasi-conformal mappings of curvilinear polygonal regions bounded by uncertain streamlines and equipotential lines. The feature of the method proposed is that the summary representation formulae allow to explicitly write the solution to the localized linear (main) part of the obtained system of equations. The unknown coefficients are determined here by solving a non-linear system generated solely by the boundary conditions and numerical analogues of the Cauchy–Riemann equations.