Application of a 2D BEM-Level Set Domain Decomposition to the Green-Water

A Domain-Decomposition strategy for the study of nonlinear air-water interface problems has been developed and presented to the last workshop (see Colicchio et al. 2004b). The method is based on the use of a Boundary Element Method (BEM) and a Navier-Stokes solver combined with a Level-Set technique to capture the interface evolution (NS-LS). Both solvers are accurate to the second order both in space and in time. The two solution techniques are applied to simulate the air-water evolution in different portions of the fluid domain. In particular, the NS-LS analyzes the regions that can be characterized by breaking and fragmentation of the interface, vortex shedding and air entrainment phenomena. The BEM is adopted in the rest of the domain of interest. Many practical problems in ship hydrodynamics exist where such kind of zonal approach can be adopted. An example is the water on deck caused by the vessel interaction with pre-existing waves. In this case the field solver is needed to describe all the stages of the water evolution onto the deck and near the vessel. The challenge in a zonal method is the proper exchange of information between the two solvers across the common bound-aries. This has been obtained enforcing an explicit coupling instead of using an iterative technique (see i.e. Quarteroni and Valli 1999). The details of the developed strategy are described in Colicchio et al. (2004a). These involve both a Domain-Decomposition step, where the data from one solver, say donator, are transfered to the other one, say receiver, and a Domain-Composition step, necessary to make the information from the donator consistent with the receiver. Due to these features, the resulting method has been named as Domain-Decomposition Domain-Composition strategy (DDDC)