Arbitrary Lagrangian–Eulerianc finite element method for unsteady, convective, incompressible viscous free surface fluid flow

In this paper, free surface flow problems involving large free surface motions are analysed using finite element techniques. In solving these problems an arbitrary Lagrangian‐Eulerian (ALE) kinematical description of the fluid domain is adopted, in which the nodal points can be displaced independently of the fluid motion. This formulation leads to an easy and accurate treatment of fluid‐fluid interfaces, and greater distortions in the fluid motions can be handled than would be allowed by a purely Lagrangian method. This paper describes the basic methodology, presents finite element approximations and discusses such matters as stability, accuracy and rezoning. The generality and the advantage of the present method are discussed, and its versatility is demonstrated through a few numerical experiments.