QUASI-SINGULAR INTEGRALS IN THE MODELING OF NONLINEAR WATER-WAVES IN SHALLOW-WATER

The model by Grilli et al.,5,8 based on fully nonlinear potential flow equations, is used to study propagation of water waves over arbitrary bottom topography. The model combines a higher-order boundary element method for the solution of Laplace's equation at a given time, and La grangian Taylor expansions for the time updating of the free surface p osition and potential. In this paper, both the accuracy and the effici ency of computations are improved, for wave shoaling and breaking over gentle slopes, in domains with very sharp geometry and large aspect r atio, by using quasi-singular integration techniques based on modified Telles17 and Lutz11 methods. Applications are presented that demonstr ate the accuracy and the efficiency of the new approaches.