Shoreline motion in nonlinear shallow water coastal models

Abstract

Different shoreline boundary conditions for numerical models of the Non-Linear Shallow Water Equations based on Godunov-type schemes are compared. The study focuses on the Peregrine and Williams [Peregrine, D.H., Williams, S.M., 2001. Swash overtopping a truncated plane beach. Journal of Fluid Mechanics 440, 391–399.] problem of a single bore collapsing on a slope. This is considered the best test to assess performances of the shoreline boundary treatments in terms of all the parameters of interest in swash zone modelling. Emphasis is given to the shoreline trajectory and flow velocity modelling. A mismatch of the velocity at the early stage of the motion is highlighted. Most of the tested techniques perform similarly in terms of maximum run-up, the backwash phase is critical in all cases. Starting from the Brocchini et al. [Brocchini, M., Bernetti, R., Mancinelli, A., Albertini, G., 2001. An efficient solver for nearshore flows based on the WAF method. Coastal Engineering 43(2), 105–129.] shoreline boundary treatment, a simple technique that improves the accuracy of velocity predictions is also developed. A sensitivity analysis of the domain resolution and the threshold value of the water depth that defines a wet cell is also presented.