A solution method for two-dimensional potential flow about bodies with smooth surfaces by direct use of the boundary integral equation

Abstract

This work presents a novel boundary integral method to treat the two-dimensional potential flow due to a moving body with the Lyapunov surface. The singular integral equations are derived in singularity-free form by applying the Gauss flux theorem and the property of the equipotential body. The modified formulations are amenable to computation by directly using quadrature formulae. Instead of the conventional boundary element approach, the boundary surface is initially expressed in a parametric form. Further, applying the double exponential formula and the cubic spline method yield the corresponding geometrical coefficients which are involved in parametric form. For illustration, the flow field induced by a translating ellipse is examined. Numerical calculations indicate that the proposed method is more efficient than the flat-element constant-source boundary element method. Copyright © 1999 John Wiley & Sons, Ltd.