Modeling boundary-layer transition in direct and large-eddy simulations using parabolized stability equations.

We examine the potential of the nonlinear parabolized stability equations (PSE) to provide an accurate yet computationally efficient treatment of the growth of disturbances in H-type transition to turbulence. The PSE capture the nonlinear interactions that eventually induce breakdown to turbulence and can as such identify the onset of transition without relying on empirical correlations. Since the local PSE solution at the onset of transition is a close approximation of the Navier-Stokes equations, it provides a natural inflow condition for direct numerical simulations (DNS) and large-eddy simulations (LES) by avoiding nonphysical transients. We show that a combined PSE-DNS approach, where the pretransitional region is modeled by the PSE, can reproduce the skin-friction distribution and downstream turbulent statistics from a DNS of the full domain. When the PSE are used in conjunction with wall-resolved and wall-modeled LES, the computational cost in both the laminar and turbulent regions is reduced by several orders of magnitude compared to DNS.