A sharp cartesian method for the simulation of air-water interface

We firstly present a sharp cartesian method for the simulation of incompressible flows with high density and viscosity ratios, like air-water interfaces. This method is inspired from the second-order cartesian method for elliptic problems with immersed interfaces developed in [1]. Then, because a high-order interface description is necessary in this context, we present a level-set technique allowing to maintain in the course of time a third-order accuracy of the level-set itself, and thus a first order accuracy of the curvature