A Strongly-coupled Non-parametric Integral Boundary Layer Method for Aerodynamic Analysis with Free Transition

Abstract

© 2019, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved. The integral boundary layer (IBL) method with viscous-inviscid coupling is an effective tool for rapid aerodynamic design and analysis. However, existing IBL methods remain to be extended to general three-dimensional (3D) configurations. To this end, previous work proposed an IBL formulation using the discontinuous Galerkin (DG) finite element method (FEM) with strong viscous-inviscid coupling, which is non-parametric in the sense that the aerodynamic shape is does not have to be explicitly parametrized by curvilinear coordinates. The current work builds on that strongly-coupled non-parametric IBL formulation, and further develops numerical discretization methods to enable flow transition modeling. Both a cut-cell-based fitted transition approach and a simple captured transition approach are presented and compared. In solving the nonlinear system of equations arising from free-transition problems, a strongly-coupled global Newton solver is adopted and augmented for solution robustness. Numerical results demonstrate favorable accuracy and robustness of the cut-cell fitted transition method compared to the captured transition methods. On the other hand, the captured transition approach allows for a more straightforward numerical implementation, but requires further improvement to achieve comparable reliability for aerodynamic analysis with free transition.