Numerical methods for water‐wave radiation problems

Abstract

AbstractA boundary integral equation method is used to compute the forces acting on bodies oscillating at or near the free surface of a fluid. This method relies on the use of a Green function representing the potential of a unit pulsating source beneath the free surface. A peculiarity of the boundary integral equation method in the presence of a free surface is that it breaks down at certain characteristic frequencies also known as ‘irregular frequencies’. The objectives of the present study are to develop simple and efficient algorithms for the numerical evaluation of the Green function as well as a method for removing the irregular frequencies. In particular, systematic expansions for the Green function have been developed. These algorithms are very efficient and remarkably simple to implement numerically. In order to remove the irregular frequencies, the boundary integral equation is supplemented by the first N null‐field equations. As a result the first N irregular frequencies are eliminated. This method introduces a very small additional computational cost and is general enough so that it can be applied to any free surface problem.