ISSN 2542–0380
Труды Института механики им. Р.Р. Мавлютова
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Proceedings of the Mavlyutov Institute of Mechanics


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Zhitnikov V.P., Zinnatullina O.R., Fedorova G.I. Investigation of solutions of non-stationary Hele-Shaw problems by means of a numerical filtration Proceedings of the Institute of Mechanics of Ufa Branch of RAS. 6 (2008). 68–74.
2008. Vol. 6. Issue 1, Pp. 68–74
URL: http://proc.uimech.org/uim2008.1.009,en
DOI: 10.21662/uim2008.1.009
Investigation of solutions of non-stationary Hele-Shaw problems by means of a numerical filtration
Zhitnikov V.P., Zinnatullina O.R., Fedorova G.I.
Ufa state aviation technical university, Ufa

Abstract

The problem on each time step is reduced to the solution of three boundary problems for definition of analytical functions of complex variable: conformal mapping of parametric variable region on the physical plane, Dirichlet's problem for determination of intensity of electric field and Riemann – Hilbert's problem for calculation of partial derivatives on time of coordinates of interelectrode space points. Approximation by spline functions is made, the algorithms of the solution of non-stationary problems differing from known by the accuracy and stability are described. Results of the numerical solution are represented.

Keywords

Laplace equation,
numerical-analytical method,
numerical filtration