A geometry aware arbitrary order collocation Boundary Element Method solver for the potential flow past three dimensional lifting surfaces

TL;DR

This paper introduces a geometry-aware collocation Boundary Element Method solver for potential flow past 3D lifting surfaces, utilizing a Galerkin variational approach for improved accuracy and flexibility with arbitrary order elements.

Contribution

It develops a novel BEM-based solver that incorporates Galerkin formulations and arbitrary order elements, enhancing accuracy and compatibility with CAD models for 3D lifting surface analysis.

Findings

Accurately predicts flow around wings with NACA 0012 airfoils.

Demonstrates improved accuracy with grid refinement and higher discretization order.

Reproduces experimental data effectively for various wing configurations.

Abstract

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.