This work presents a numerical model for the simulation of potential flow past three dimensional lifting surfaces. The solver is based on the collocation Boundary Element Method, combined with Galerkin variational formulation of the nonlinear Kutta condition imposed at the trailing edge. A similar Galerkin variational formulation is also used for the computation of the fluid velocity at the wake collocation points, required by the relaxation algorithm which aligns the wake with the local flow. The use of such a technique, typically associated with the Finite Element Method, allows in fact for the evaluation of the solution derivatives in a way that is independent of the local grid topology. As a result of this choice, combined with the direct interface with CAD surfaces, the solver is able to use arbitrary order Lagrangian elements on automatically refined grids. Numerical results on a rectangular wing with NACA 0012 airfoil sections are presented to compare the accuracy improvements obtained by grid spatial refinement or by discretization degree increase. Finally, numerical results on rectangular and swept wings with NACA 0012 airfoil section confirm that the model is able to reproduce experimental data with good accuracy.

翻译：本文提出了一种用于模拟三维升力面势流的数值模型。该求解器基于配点边界元法，并结合了施加于后缘的非线性Kutta条件的Galerkin变分形式。类似的Galerkin变分形式也被用于计算尾流配点处的流体速度，这是由使尾流与当地流动对齐的松弛算法所必需的。这种通常与有限元法相关的技术的使用，实际上允许以独立于局部网格拓扑的方式求解解的导数。由于这一选择，加之与CAD曲面的直接接口，该求解器能够在自动细化的网格上使用任意阶拉格朗日单元。文中展示了具有NACA 0012翼型截面的矩形机翼的数值结果，以比较通过网格空间细化或离散化阶数提高所获得的精度改进。最后，具有NACA 0012翼型截面的矩形和后掠机翼的数值结果证实，该模型能够以良好的精度复现实验数据。