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Numerical Modelling of Equilibrium Capillary Surfaces: Some Methods and Results

by Polevikov, Viktor K..

Series: 1998-10, Preprints


A new iteration-difference approach is proposed for numerical
solving flat and axisymmetric problems on equilibrium shapes of a capillary surface
called the tangential method or the T-method in virtue of
constructional features. This method possesses a high order
of approximation on a nonuniform grid, simple algorithm,
improved agreement between an iteration solution and an exact solution
of a different problem.
A condition for iteration convergence is obtained within the framework
of a linear theory. As a result of tests, it is revealed
that the proposed method is more economic as against other
iteration-difference schemes and much exceeds them in computational
stability. It is found that it adequately responds to physical
collapse of equilibrium shapes, i.e. it can be adopted to
investigate stability of equilibrium states of a capillary surface.