Finite element method for free surface flow problems

A numerical method for solving boundary value problems related to incompressible irrotational and inviscid flow with free surface is introduced in this paper. The free surface is generated by a flow past a rigid body piercing the free surface or lying at the bottom. Optimal control techniques are used to satisfy the dynamic condition at the free surface. For problems related to flow past a body piercing the free surface, one of the main difficulties is the singularity at the contact region between the free surface and the body, when solving for the fluid motion. Due to the fact that the pressure at the body is unknown, mixed boundary conditions have to be used: the kinematic condition at the wetted surface of the body, and dynamic condition at the free surface. In this paper, a finite element formulation is developed to circumvent this difficulty. A uniform boundary condition, the kinematic condition, is applied at the free surface and the wetted surface of the body.