Added Masses and Forces on Two Bodies Approaching Central Impact in an Inviscid Fluid

An integral-equation procedure has been developed to determine interaction forces on two bodies approaching central impact in an inviscid fluid. The accuracy of the results from that procedure is evaluated by applying it to a pair of circles and a pair of spheres for which exact solutions are available. A second purpose was to refine the procedure so that accurate solutions could be obtained at closer distances between the bodies. In the first part of this work, the classical theory is extended by deriving truncation corrections for the infinite series representing the exact solution and asymptotic formulas for computing interaction forces at small gaps. In the second part, two problems were resolved: one on the treatment of the sharp peaks of the integrands when the gap between the bodies was small, the other on reducing the errors in the numerical differentiation required to evaluate the forces. Results for various combinations of circle pairs, for equal spheres, and for an elliptical cylinder approaching a circular one are presented. A new relation between the interaction forces on a wall and on a body moving normal to it is presented. Addendum published in 1994 Volume 38, Issue 2 (June), pages 172–173, is included.