An ALE/FE formulation for high precision interface tracking in separated multiphase flows

We present an Arbitrary Lagrangian Eulerian/Finite Element (ALE/FE) formulation to simulate flows with sharp interfaces between several fluids or phases. The proposed numerical approach relies on the explicit representation of interfaces as a collection of inner mesh edges and the direct tracking of the time evolution of these interfaces. The ALE/FE formulation allows for the use of high-order time integrators within a hp-adaptive time integration procedure already developed for single phase flows. The kinematic and dynamic conditions across interfaces are enforced with the use of zero-thickness interfacial finiteelement along interfaces. We consider both linear (P1) and quadratic (P2) finite element discretization. The simulation of very large deformation of interfaces is rendered possible by the use of an adaptive remeshing algorithm. The method is applied to the prediction of the propagation of solitary waves in basins with constant and variable bathymetry as well as the simulation of the Rayleigh-Taylor instability.