Numerical Implementation of Nonstationary Axisymmetric Problems of an Ideal Incompressible Fluid with a Free Surface

Abstract

A fundamentally new unsaturated technique for the numerical solution of the Dirichlet–Neumann problem for the Laplace equation was developed. This technique makes it possible, due to the smoothness of the sought solution of the problem, to take into account the axisymmetric specificity of the problem which is an insurmountable obstacle to any saturated numerical methods, i.e., methods with a leading error term.