Coupling Level Set Methods With Boundary Integral Methods For Free Surface Potential Flows

Non viscid and rotational free fluid flows in moving domains can be used to model various physical phenomenons such us wave breaking, droplet and bubble break up dynamics and electrostatically charged drop distortion, among others.The classical lagrangian fully non linear potential flow model can be recasted in a complete Eulerian formulation using the Level Set approach. The coupled system of partial differential equations is approximated using a Boundary Integral method, to calculate the moving front velocity, and the Level Set method to update the position of the front. The numerical methods involved are: a linear Boundary Element method for the laplacian equation and first order upwind schemes for the Level Set hyperbolic equations. This novel approach has turn out to be very robust and versatile, due to the capability of the Level Set method to handle topological changes of the moving domain.Full details of how to arrive to the Eulerian formulation of the model equations will be presented and the numerical schemes of the coupled system will be also described. Several computational results will be addressed: The propagation and shoaling of a solitary wave over a sloping beach and the collapse of an infinite fluid column under the action of surface tension forces. Recent results on the evolution and distortion of charged droplets and subsequent Coulombic fission will be presented in more detail