Affiliation:
1. 1Belorussian State University, Department of Computional Mathematics,4 F. Skaryna Ave., 220050 Minsk, Belarus.
Abstract
Abstract 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.
Subject
Applied Mathematics,Computational Mathematics,Numerical Analysis
Cited by
10 articles.
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