Oscillatory Subsonic Piecewise Continuous Kernel Function Method

Abstract

Theme T WO main methods currently are employed in the prediction of the aerodynamic forces acting on lifting surfaces at subsonic flow. These methods inlcude the subsonic kernel function approach, which assumes pressure polynomials to describe the pressure field over the wing, and the finite-element approach, such as the doublet lattice method (DLM) or the vortex lattice method (VLM). The kernel function method (KFM), when based on orthogonal polynomials and carefully determined collocation points, shows a rapid convergence of its solution (with a small number of pressure polynomials) provided that the pressure field over the wing is smooth. Pressure discontinuities, such as those arising from control surface rotations, can be treated successfully using the KFM only when the exact shape of the singularity is known. The overlooking of pressure singularities using the KFM leads to a rapid deterioration in the convergence of the solution and to a general loss in the effectiveness of the method. The finite-element methods (FEM) can cope successfully with unknown pressure singularities provided that their location is known. The FEM, however, require a relatively large number of unknowns for convergence, leading at times to a relatively large residual error at the converged values. In the present paper a method is presented, similar to the one described in Ref. 4 in connection with mixed transonic flow, which combines the rapid convergence characteristics of the KFM with the ability of the FEM to treat discontinuities without having to determine their exact form. The method is tested using a two-dimensional airfoil problem (with control surfaces and gaps) with the intention of establishing its merits before embarking on its extension to the three-dimensional flow case.