Simulating an H-type transitional boundary layer in a coupled NLPSE and WMLES framework with a Falkner-Skan wall model

Numerical simulation of wall-bounded flows poses significant challenges, especially when considering flows that include a combination of laminar, transitional, and turbulent regimes. Failure to resolve the laminar and transitional regions properly can result in substantial errors when predicting mean quantities of interest, such as lift and drag. For wall-modeled large-eddy simulations (WMLES) in particular, it has been observed that the laminar and transitional regions may necessitate 10-100 times more grid points than the turbulent region (Slotnick et al., 2014) to adequately capture the amplification of disturbances that lead to transition. In this work, we will demonstrate that a nonlinear parabolized stability equation solver can be coupled with a WMLES solver to reduce the computational cost of accurately simulating an H-type transitional flat-plate boundary layer, relative to direct numerical simulation. Additionally, we show that the necessary mesh resolution in the laminar portion of the boundary layer can be reduced with the implementation of a Falkner-Skan wall model (Gonzalez et al., 2020).