A pFFT Accelerated BEM Linear Strength Potential Flow Solver

In this paper the development of a linear shape function, Galerkin Boundary Element Method (BEM) for solving the direct potential flow integral equation around arbitrary 3-Dimensional bodies is described. The solution of the potential flow for both constant and linear shape functions over a triangulated body surface is examined. In order to facilitate a larger and more practical number of panels, an iterative GMRES [1] matrix solution method is coupled with a precorrected Fast Fourier Transform (pFFT) approximate matrix vector product (MVP)[2]. The pFFT algorithm is described and the differences in attaining MVP’s for linear and constant strength panel distributions are highlighted. A simple flat sheet wake model is included to solve the lifting body problem. The pFFT is shown to reduce the solution time to O(nlog(n)) operations (n is the number of panels). The results from flat panel surface representations of the body show that the convergence rate of the solution is at best O(n) for both linear and constant basis function representations of the solution. When the constant basis solution is sampled at the centroid of the panel, the error converges at a similar rate to the linear basis solution error, namely (O(n)); however, when the solution is sampled at surface points other than the centroid, the constant basis representation will converge at a slower rate O(n^1/2), while the linear basis solution converges at a rate of O(n) for all points on the body.