Numerical Solutions for Some Free Boundary Value Problems Occuring in Planar Fluid Dynamics

Abstract

In the paper [1], we consider the solvability of some free boundary value problems occuring in planar fluid dynamics. The object of the present paper is to present numerical methods for solving free boundary problems. It was shown in [1] that such free boundary problems may be transformed into a mixed boundary value problem for a linear or nonlinear elliptic complex equations, which in turn, might be reformulated into a conformal mapping or quasiconformal mapping from a general domain onto some canonical domain. In this paper we direct our discussion to the numerical solution of mixed boundary value problems for generalized Beltrami equations.