A 3D shock-capturing model for free surface flow

In this paper a non-hydrostatic and shock-capturing model for the simulation of wave-structure interaction and hydrodynamic phenomena (wave refraction, diffraction, shoaling and breaking) is proposed. The model is based on an integral formulation of the motion equations which are solved on a time dependent curvilinear coordinate system: a coordinate transformation maps the varying coordinates in the physical domain to a uniform transformed space. The motion equations are discretized by means of a shock-capturing numerical procedure based on high order WENO reconstructions. The solution procedure for the motion equations uses a five stage four order accurate Runge-Kutta (SSPRK) fractional- step method and applies a pressure corrector formulation in order to obtain a divergence-free velocity field at each stage. The proposed model is validated against two benchmark test cases and is used in order to analyse the effects that a submerged breakwater produces on wave motion.