St. Grilli et R. Subramanya, QUASI-SINGULAR INTEGRALS IN THE MODELING OF NONLINEAR WATER-WAVES IN SHALLOW-WATER, Engineering analysis with boundary elements, 13(2), 1994, pp. 181-191
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.