Local Error Analysis of Three-Dimensional Panel Methods in Terms of Curvilinear Surface Coordinates

Abstract

To solve three-dimensional incompressible potential flow problems, panel methods or boundary element methods can be used. These are based on integral equations representing source and dipole distributions over the fluid boundary. The integral equations are expressed in terms of general curvilinear surface coordinates, which serve as coordinates in the computational domain. This paper presents a method of obtaining consistent approximations to the resulting analytical expressions. Estimates of the order of magnitude of the local truncation errors are given. It is shown that, to obtain an $O(\Delta ^3 )$ local truncation error for the potential integrals, a linear source distribution, a quadratic dipole distribution, and a quadratic surface approximation are needed. The same approximations are needed to obtain an $O(\Delta ^2 )$ truncation error in the approximation of the velocity integrals.