Tracking surfaces is a challenging issue for a realistic simulation of fluids in interaction with other fluids or solid objects. Level set methods is the state of the art methodology to discretize the movement of a surface in any kind of flow field, by representing it as a scalar variable that is advected by numerical schemes similar to the advection of passive tracers. Here, we apply level set methods to a Boussinesq model, in order to simulate air and water as it moves around its horizontally stratified equilibrium position. The numerical model tends to mix air and water in the presence of shear instability and resulting intermediate densities are unrealistic for air and water. In order to track the water surface, a level set function is implemented. To reduce unrealistic mixing a relaxation approach is proposed: Densities that differ from that of air and water are slightly but consequently restored back to its reference value. Challenges remain in the optimization of this method: A weak relaxation hardly reduces mixing, whereas strong relaxation tends to result in unphysical behaviour.
An example without the level-set implementation, where the two fluid tend to mix
Implementing the level-set methods and using the relaxation approach, yields in contrast