caa a22 4500 378884115 CHVBK 20180305123438.0 cr unu---uuuuu 161128s2004 xx s 000 0 eng 10.2478/cmam-2004-0005 doi (NATIONALLICENCE)gruyter-10.2478/cmam-2004-0005 Polevikov Victor K. Belorussian State University, Department of Computional Mathematics,4 F. Skaryna Ave., 220050 Minsk, Belarus. Methods for Numerical Modeling of Two-Dimensional Capillary Surfaces [Elektronische Daten] [Victor K. Polevikov] Certain methods for numerical solving plane and axially symmetric problems on equilibrium shapes of a capillary surface are presented. The methods possess a high order of approximation on a nonuniform grid. They are easy to realize, fairly universal and suitable for constructing not only simply connected but also doubly connected and disconnected surfaces, including strongly curved ones. It is shown that the iterative algorithms constructed are absolutely stable at each iteration. The condition for convergence of iterations is obtained within the framework of a linear theory. To describe peak-shaped configurations of a magnetic uid in a high magnetic field, an algorithm of generation of adaptive grid nodes in accordance with the surface curvature is proposed. The methods have been tested for the well-known problems of capillary hydrostatics on equilibrium shapes of a drop adjacent to the horizontal rotating plate under gravity, and of an isolated magneticuid drop in a high uniform magnetic field. It has been established that they adequately respond to the physical phenomenon of a crisis of equilibrium shapes, i.e., they can be adopted to investigate the stability of equilibrium states of a capillary surface. This article is distributed under the terms of the Creative Commons Attribution Non-Commercial License, which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited. capillary surface nationallicence parametric differential equations nationallicence numerical modeling nationallicence finite-difference method nationallicence tangential method nationallicence spline-method nationallicence computational stability nationallicence convergence of iterations nationallicence adaptive grid nationallicence test problems nationallicence computational experiment nationallicence Computational Methods in Applied Mathematics De Gruyter 4/1(2004), 66-93 1609-4840 4:1<66 2004 4 cmam https://doi.org/10.2478/cmam-2004-0005 text/html Onlinezugriff via DOI 1 research article jats NATIONALLICENCE 856 40 https://doi.org/10.2478/cmam-2004-0005 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Polevikov Victor K. Belorussian State University, Department of Computional Mathematics,4 F. Skaryna Ave., 220050 Minsk, Belarus NATIONALLICENCE 773 0- Computational Methods in Applied Mathematics De Gruyter 4/1(2004), 66-93 1609-4840 4:1<66 2004 4 cmam CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-gruyter