Spatial variations in numerical wave tanks with active wave generating–absorbing system

Abstract

Wave–structure interaction can be investigated in detail by numerical experiments, such as Navier–Stokes solvers with Volume Of Fluid models to capture the free surface. The quality of the wave field in such Numerical Wave Tanks largely depends on the boundary conditions to generate or/and absorb the waves. In case of regular waves, instead of obtaining a uniform wave field throughout the wave tank, spatial variations in crest height and trough depth are found with beat lengths smaller than the wave length. In this paper, three different wave absorbing boundary conditions are investigated for their effects on the wave field uniformity: the Original Sommerfeld Boundary Condition, a Generalized Sommerfeld Boundary Condition, and a method including Relaxation Zones. An extensive analysis, involving the decomposition of the waves into incident and reflected waves at first order and higher order harmonics is required to explain the phenomenon of spatial variations. It is concluded that Relaxation Zones provide the most spatially uniform wave fields, at the cost of larger computational domains. The spatial variations in the Original and Generalized Sommerfeld Boundary Conditions are found to also be contributed from the superposition of the second order incident bound waves and the second order reflected free waves. This effect is found to be more significant for steeper waves. A graded mesh method at the absorbing side of the tanks is proposed to minimize the spatial variations.