ASPECTS ABOUT THE EVALUATION OF THE SINGULARITIES WHEN APPLYING THE BOUNDARY ELEMENT METHOD TO SOLVE PROBLEMS OF FLUID FLOW AROUND BODIES

Abstract

One of the most powerful numerical techniques used to solve boundary values problems for fluid mechanics is the boundary element method. When solving a problem with this method there have to be made two important steps: first, we must obtain an equivalent boundary formulation for the problem involved, in fact a boundary integral equation, and then, this boundary integral equation which is a singular one must be solved. The Boundary Element Method reduces the problem to a system of linear equations. The diagonal coefficients of the system the problem is reduced at come from singular integrals and in order to obtain a well conditioned problem their evaluation has to be made with great attention. The paper presents some methods of treating the singularities that appear when the boundary element method with different types of isoparametric boundary elements is used to solve 2 and 3-dimensionall problems of fluid flow around bodies. Based on the numerical results obtained a comparison study between different methods is made and it points out the advantages of some methods on others. For solving some of the problems presented there are used constant, linear and quadratic boundary elements.