A Third-Order BEM for Potential Aerodynamics

The aim of this paper is the presentation of a higher-order BEM formulation for the solution of potential aerodynamics. For simplicity, here we limit ourselves to incompressible flows, which are governed by the Laplace equation. The proposed formulation is particularly attractive because of its user-friendliness, and is applicable to other problems governed by the Laplace equation. Specifically, we have developed a third-order algorithm, i.e., an algorithm resulting in a bicubic distribution on each element for all the variables involved in the problem under consideration. Such an algorithm has been developed in order to obtain three main goals: (i) a smooth solution (specifically having a velocity continuous at the nodes); (ii) a topological structure for the geometrical discretization that is user friendly, i.e., as simple as possible (specifically, as simple as a first-order discretization); (iii) a solution that is described in terms of a limited number of parameters (specifically the values assumed by the unknown at the grid nodes).