A numerical model has been proposed to solve fluid flows with complex free surfaces in two and three space dimensions. The unknowns are the volume fraction of liquid in the whole cavity containing the fluid, the velocity and pressure in the liquid. A splitting algorithm is used to decouple advection phenomena to diffusion phenomena. Advection is solved using the forward characteristics method on a fine grid of rectangular cells. Diffusion is solved using simple finite elements on a tetrahedral mesh of the cavity.
The model has been successfully applied to mould filling situations. It can be modified in order to take into account the case when bubbles of gas are trapped into the liquid. The model has also been successfully extended to viscoelastic flows in complex domains. Complex experiments such as the stretching of a filament or jet buckling have been reproduced.
Mathematical and numerical analysis of simplified models have been performed.
Below is an example of non-Newtonian flows simulation with different physical properties.
Below is an example of S-shape cavitiy filling with bubble creation.