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Prikladnaya Mekhanika i Tekhnicheskaya Fizika, 2009, Volume 50, Issue 4, Pages 87–99
(Mi pmtf1769)
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This article is cited in 2 scientific papers (total in 2 papers)
Determining the limiting solutions of nonstationary axisymmetric Hele–Shaw problems
V. P. Zhitnikov, O. R. Zinnatullina, S. S. Porechny, N. M. Sherykhalina Ufa State Aviation Technical University, Ufa, 450000, Russia
Abstract:
Numerical solution of the Hele–Shaw problem reduces to solution of three boundary-value problems of determining analytic functions of a complex variable in each time step: conformal mapping of the range of the parametric variable to the physical plane, the Dirichlet problems for determining the electric-field strength, and the Riemann–Hilbert problem for calculating partial time derivatives of the coordinates of points of the interelectrode space (the images of the points on the boundary of the parametric plane are fixed). Unlike in the two-dimensional problem, the electric-field strength is determined using integral transformations of an analytic function. Approximation by spline function is performed, and more accurate and steady (than the well-known ones) general solution algorithms for the nonstationary axisymmetric problems are described. Results of a numerical study of the formation of stationary and self-similar configurations are presented.
Keywords:
axisymmetric Hele-Shaw problem, nonstationarity, numerical investigation.
Received: 17.12.2007 Accepted: 14.05.2008
Citation:
V. P. Zhitnikov, O. R. Zinnatullina, S. S. Porechny, N. M. Sherykhalina, “Determining the limiting solutions of nonstationary axisymmetric Hele–Shaw problems”, Prikl. Mekh. Tekh. Fiz., 50:4 (2009), 87–99; J. Appl. Mech. Tech. Phys., 50:4 (2009), 617–627
Linking options:
https://www.mathnet.ru/eng/pmtf1769 https://www.mathnet.ru/eng/pmtf/v50/i4/p87
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