Quasi-singular integrals in the modeling of nonlinear water waves in shallow water

Abstract

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 Lagrangian Taylor expansions for the time updating of the free surface position and potential. In this paper, both the accuracy and the efficiency of computations are improved, for wave shoaling and breaking over gentle slopes, in domains with very sharp geometry and large aspect ratio, by using quasi-singular integration techniques based on modified Telles 17 and Lutz 11 methods. Applications are presented that demonstrate the accuracy and the efficiency of the new approaches.