Implementation of Adaptive Gaussian Quadrature for Improved Accuracy of Boundary Element Methods Applied to Three Dimensional Geometries

Abstract

An adaptive Gaussian quadrature method for characterizing flow over three dimensional bodies via a boundary element method using isoparametric quadrilateral elements with non-constant source and dipole strengths has been developed and tested. This method is compared to state-of-the-art methods: flat elements with constant strengths, flat elements with bilinear strengths, and twisted elements with constant dipole strengths. As such, an overview of current boundary element methods is provided. The method developed here for twisted elements with non-constant source and dipole strengths is advantageous in that it both better approximates the actual geometry of the surface and the distribution of the dipole and source strengths. The majority of current methods are lacking at least one of these attributes. The developed method has been validated by comparison to two known analytical solutions: a non-lifting ellipsoid and a Kármán-Trefftz airfoil. The flexible and robust procedure presented here results in improved accuracy of the solution to the Laplace equation around three dimensional bodies.