ASYMPTOTIC CONVERGENCE OF HIGHER-ORDER ACCURATE PANEL METHODS

Error analysis of incompressible potential flow solutions suggests that current panel methods employing piecewise quadratic doublet distributions, in combination with a Dirichlet boundary condition, can predict surface velocities within an error that vanishes proportionally to the third power of the panel size when panels are made arbitrarily small. This error analysis is based on computational experiments performed for a two-dimensional airfoil with a finite trailing-edge angle. The governing differential equation is Laplace's equation describing incompressible flow. The findings from the computational experiments are consistent with the observation that the corresponding low-order accurate panel methods, employing piecewise constant doublet distributions, yield a numerical approximation to the surface velocity that is accurate to first order in the panel size, when the size of the panels tends to zero.