Numerical simulation of free-surface flows

A numerical procedure based on the Arbitrary Lagrangian- Eulerian (ALE) description of flow is developed to simulate free surface problems. The conservation equations are rewritten using a referential kinematic description where the grid points move independently of the fluid particles. In the applications considered in this work, the fluid domain is bounded below by a rigid impermeable wall and above by a vapor-liquid moving interface. The free surface is taken to be resting on vertical spines and the grid points slide up and down along the vertical spines. The two-dimensional unsteady Navier-Stokes equations are discretized in time using Chorin type Projection scheme and pressure is determined from the Poisson equation. Galerkin Finite Element Method with three node triangular elements has been used for spatial discretization. The turbulence is modeled using two-equation k-epsilon closure model. The phase transition from supercritical flow regime to subcritical flow regime is investigated in greater detail. In this paper the mathematical theory behind these modifications is described. Some of the unique features of the numerical methods that are being used for the solution of the resultant equations are also presented.