Modelling coastal water waves using a depth-integrated, non-hydrostatic model with shock-capturing ability

Abstract

ABSTRACTThis paper presents a depth-integrated, non-hydrostatic model for coastal water waves. The shock-capturing ability of this model is its most attractive aspect and is essential for computation of energetic breaking waves and wet–dry fronts. The model is solved in a fraction step manner, where the total pressure is decomposed into hydrostatic and non-hydrostatic parts. The hydrostatic pressure component is integrated explicitly in the framework of the finite volume method, whereas most of the existing models use the finite difference method. The fluxes across the cell faces are computed in a Godunov-based manner through an efficient multi-stage scheme. The flow variables are reconstructed at each cell face to obtain second-order spatial accuracy. Wave breaking is treated as a shock by locally switching off the non-hydrostatic pressure in the wave front. A moving shoreline boundary is also incorporated. The robustness and accuracy of the developed model are demonstrated through numerical tests.