Outflow Boundary Conditions for Spatial Navier-Stokes Simulations of Transition Boundary Layers

For numerical simulations of the spatially evolving laminar-turbulent transition process in boundary layers using the complete Navier-Stokes equations, the treatment of the outflow boundary requires special attention. The disturbances must pass through this boundary without causing reflections that would significantly alter the flow upstream. In this paper, we present various methods to influence the disturbed flow downstream of the region of interest, such that the disturbance level at the outflow boundary is significantly reduced, and hence the possibility of reflections is minimized. To demonstrate the effectiveness of the various techniques to alter the disturbance flow near the outflow boundary, the fundamental breakdown of a strongly decelerated boundary layer is simulated. Our results show that the most effective method is to spatially suppress the disturbance vorticity within a so-called "relaminarization zone." The suppression of the disturbance vorticity is gradually imposed within this zone by means of a weighting function. The enforced decay of the disturbance vorticity leads to a practically complete dissipation of any fluctuating component. Most importantly, this technique causes only a negligible upstream effect. The "relaminarized" boundary-layer flow then passes through the outflow boundary without significant reflections.