An Integral Boundary Layer Method using Discontinuous Galerkin Discretization and Captured Transition Modeling

© 2020, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved. Viscous analysis is crucial for understanding aerodynamic performance metrics such as profile drag. For three-dimensional (3D) viscous analysis, Reynolds-averaged Navier-Stokes (RANS) solvers are often the fastest available tool in practice but the required computational efforts preclude its extensive use for preliminary design. In contrast, the integral boundary layer (IBL) method offers a computationally more efficient alternative with comparable effectiveness when applicable. However, existing IBL methods mostly rely on two-dimensional (2D) or quasi-2D assumptions and thus remain to be extended to a fully 3D formulation for general configurations. To this end, we continue the development of an IBL method with discontinuous Galerkin (DG) finite element discretization and strong viscous-inviscid coupling. The current work proposes a captured laminar-to-turbulent flow transition treatment for the IBL method that can be more conveniently extended to the 3D case compared to a previously examined fitted transition approach. The current captured transition treatment also leverages a more robust nonlinear solution method and achieves accurate solution of transitional flows. Moreover, correction to the standard DG discretization is introduced for well-behaved numerical solution. Numerical results of the proposed method in a 2D implementation compares well with XFOIL and demonstrate its capability for practical aerodynamic analysis with free transition