Boundary element methods for determining the fluid velocity in potential flow

Abstract

In this paper a direct method is presented for the numerical evaluation of the fluid velocity for the two-dimensional potential flow past fixed obstacles. The approach applied boundary element methods (BEM), based on Cauchy's integral formula, whereby the problem is reformulated in terms of integral equations. The use of piecewise constant, linear and quadratic polynomial approximations in these integral equations for the evaluation of the fluid velocity is described. To illustrate various features of these techniques referring to the smoothness of the obstacle's contour, tests were performed for potential flow past cylinders of two contrasting shapes — the circle and the square. In addition, tests for the potential flow around two equal parallel circular cylinders were performed in order to illustrate the applicability of the method for multiply-connected domains. Comparisons with the available analytical solutions show good agreement.