Numerical modeling of equilibrium capillary surfaces: some methods and results

Abstract

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 differential 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