Boundary Integral Equation Method for Free Surface Flow Analysis

Abstract

As a numerical technique the boundary integral equation method has a number of outstanding advantages. These include: Problems are much easier to set up; it requires less data to define the grid; it is efficient, using less computer time and storage than finite differences and finite elements; approximations are confined to the boundaries giving interior solutions with at least as much accuracy; it has better accuracy than finite differences and finite elements for equal discretization; one can use intuitive grid spacing since derivatives are not approximated; velocities are obtained without inaccurate numerical differentiation; singularities are easily handled; infinite fields are easily handled; universal programs are easy to code; it has geometric flexibility; the grid size is easy to vary; and it can use a variety of approximations to conform to the demands of the problem and the desired degree of continuity. With that list of advantages, it should be a universal method that displaces all other methods. Indeed it would except for one disadvantage: The variety of problems it can solve — or at least the variety of problems it can solve while retaining all those advantages — is small.