A pFFT Accelerated Linear Strength BEM Potential Solver

A linear strength, Galerkin Boundary Element Method (BEM) for the solution of the three dimensional, direct potential boundary integral equation is presented. The method incorporates node based linear shape functions of the single and double layers on °at triangular elements. The BEM solution is accelerated using a precorrected Fast Fourier Transform algorithm (pFFT) [1]. Due to the extended compact support of the linear basis, there exist several approaches for implementing a linear strength pFFT. In this paper, two approaches are discussed and results are presented for the simpler of the two implementations. The work presented in this paper is applied to potential °ow problems. Results are presented for °ow solutions around spheres and aircraft wings. The results of the sphere simulations are compared with analytical solutions, while the solutions for the wings are compared with 2-Dimensional results. The results indicate accurate solutions of the potential °ow around 3-Dimensional bodies. The linear basis shows improved accuracy when compared with the constant basis approach; however, the error of the linear BEM solution converges at a similar rate to the constant panels. This is due to the domination of the surface discretization error, which converges in the ̄rst order for planar element representations of curved surfaces.