The research of change in the complex velocity area in some problems of filtration theory

E. N. Bereslavskii

Matematičeskoe modelirovanie, Tome 28 (2016) no. 1, pp. 33-46.

Résumé

We study a question about possible transformations of complex flow velocity area in some problems of filtration theory depending on ranges of change constant of conformal mapping, which is contained in forms for mapping function. We examine a linear differential equation of the Fuchsian class, which conform to problem of conformal mapping circular hexagons in polar grid, typical for problems of filtration theory. It has been shown, that at fixing parameter, characterizing ratio of circles radii, constituting opposite sides of polygons in the complex flow velocity area, configuration of section appreciably depend on not only the properties of the functions, according to which design partial solution of the equation under consideration, but also depend on ranges of change constants of conformal mapping. It turns out that individual ranges of change these parameters may conform different on their configurations sections, which is demonstration transformation of filtration fluid flows depending on impact different physical factors and, the first of all, from evaporating rate or infiltration to the free surface.

Détail

Keywords: flow of fluid, Fuchs differential equations, conformal mappings, area of complex velocity, Jacobi elliptic functions, Theta functions.
Mots-clés : filtration, sections

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