A High-Order Finite Difference Incompressible Navier-Stokes model for Water Waves and Wave-Structure Interaction

We propose a new high-order1 finite difference numerical model for the simulation of nonlinear water waves and wave-structure interaction with fixed structures using the Navier-Stokes equations. The complete formulation is described in three spatial dimensions (3D) and preliminary validation results are here presented for two spatial dimensions (2D). A spatially fixed computational domain is defined through introducing a σ-coordinate that transform the Navier–Stokes equations long the vertical dimension from the sea bed to the still water level. Numerical experiments highlights both the correctness of the solution, the high-order convergence property that is attractive for efficient solutions as well as the classical benchmark problem due to Beji & Battjes (1994) where experimental measurements are available and hence serve as validation of the new high-order numerical scheme.