A Fourier Boundary Condition for Panel Method

Abstract

The flow of an incompressible, inviscid fluid past three-dimensional bodies can be calculated with an integral representation of the potential, using an internal Dirichlet boundary condition deduced from the external Neumann boundary condition [1]. A low order panel discretisation of the resulting equation gives rise to a set of linear equations. The matrix of which, in the case of thick bodies is usally well conditioned. Applying this method to a thin wing produces a matrix with a condition number which increases greatly with the thinness of the body and the number of panels used in the discretisation. The calculated potential becomes very inaccurate in the thin areas (i.e. near the trailing edge of wings, canards, flaps, spoilers, etc...).