Global error analysis of two-dimensional panel methods for Neumann formulation

Abstract

There are two main formulations for panel methods based on Green’s formula: Dirichlet and Neumann methods. In a previous work a rigorous analytical study of the global error of Dirichlet method was performed. In this work an analytical study of the global error is performed for the other formulation: Neumann method. The analysis is performed for a wide variety of body shapes and different panel geometries to fully understand their effect on the convergence of the method. In particular, we study the global error associated with panel methods applied to thin or thick bodies with purely convex parts or with both convex and concave parts, and with smooth or non-smooth boundaries. In order to validate the analytical results, both numerical and analytical solutions for different body geometries have been considered to compare the actual and predicted errors in each case. Finally, a comparison of the error order between both methods, Dirichlet and Neumann, has also been performed for different configurations.