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

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

“…This section briefly summarizes a 2D incompressible integral boundary layer formulation of which the detailed theory (including notation and derivation) was presented in Refs. [1,14]. Additions and modifications are elaborated in this paper which are intended to be readily generalizable to 3D boundary layers.…”

“…Full expressions of f N (H; Re θ ) and R = R(H; Re θ ) are given in Ref. [14]. They are formulated for laminar flows but do not have to be defined for turbulent flows if a fitted transition treatment such as those of Refs.…”

“…They are formulated for laminar flows but do not have to be defined for turbulent flows if a fitted transition treatment such as those of Refs. [14,15] is adopted. In favor of an alternative transition treatment, the current formulation extends the amplification factor equation ( 9) to the turbulent regime by introducing the following definitions,…”

“…On the other hand, traditional 3D boundary layer solvers depend on explicit curvilinear coordinates and are thus limited to simple geometries. This issue can be sidestepped by finite element IBL formulations [1,[10][11][12][13][14] which are applicable to general 3D configurations. Strong viscous-inviscid coupling is also a key ingredient for robust IBL methods [2,6] and Refs.…”

“…Extending Ref. [14], the current work develops a robust discontinuous Galerkin (DG) discretization for the IBL equations and a captured transition treatment that can be readily extended to general 3D cases. The transition treatment is able to utilize more robust nonlinear solution methods and to resolve flow transition accurately.…”