A Comparison of Methods for Calculating Flow About Irregular Bodies

Abstract

Calculation of the flow around aerodynamic shapes can lead to difficulties associated with ill-condi tioned matrices. These difficulties become readily apparent when one attempts to improve calculation accuracy by using more singularities to represent the flow. Another type of difficulty arises when the designer chooses a shape which is somewhat irre gular. We have found that these difficulties are alleviated when we use an over-determined set of equations obtained by using more than 2N boundary conditions for a body represented by 2N singularities along the axis. Results obtained using this least- squares approach appear to be less sensitive to local errors in body shape than the commonly used method of simultaneous equations. The problem we have consi dered involves the Fredholm equation of the first kind. It is hoped that the results obtained may have relevance to problems in electrostatics, heat conduc tion, and elasticity that involve this type of integral equation.