A three-dimensional high-order numerical model for the simulation of the interaction between waves and an emerged barrier

We present a new three-dimensional numerical model for the simulation of breaking waves. In the proposed model, the integral contravariant form of the Navier-Stokes equations is expressed in a curvilinear moving coordinate system and are integrated by a predictor-corrector method. In the predictor step of the method, the equations of motion are discretized by a shock-capturing scheme that is based on an original high-order scheme for the reconstruction of the point values of the conserved variables on the faces of the computational grid. On the cell faces, the updating of the point values of the conserved variables is carried out by an exact Riemann solver. The final flow velocity field is obtained by a corrector step which is based exclusively on conserved variables, without the need of calculating an intermediate field of primitive variables. The new three-dimensional model significantly reduces the kinetic energy numerical dissipation introduced by the scheme. The proposed model is validated against experimental tests of breaking waves and is applied to the three-dimensional simulation of the local vortices produced by the interaction between the wave motion and an emerged barrier.