Numerical simulation of free surface flows

A numerical model is presented for the simulation of complex fluid flows wi th free surfaces. The unknowns are the velocity and pressure fields in the liquid region, together with a function defining the volume fraction of liq uid. Although the mathematical formulation of the model is similar to the v olume of fluid (VOF) method, the numerical schemes used to solve the proble m are different. A splitting method is used for the time discretization. At each time step, two advection problems and a generalized Stokes problem ar e to be solved. Two different grids are used for the space discretization. The two advection problems are solved on a fixed, structured grid made out of small rectangular cells, using a forward characteristic method. The gene ralized Stokes problem is solved using a finite element method on a fixed, unstructured mesh. Numerical results are presented for several test cases: the filling of an S-shaped channel, the filling of a disk with core, the br oken dam in a confined domain. (C) 1999 Academic Press.