Efficient evaluation of the surface roughness effect on boundary layer using quasi-statically transforming roughness shape

Surface roughness has a significant influence on the boundary layer. Depending on the shape of the roughness, it sometimes triggers turbulent transition immediately and at other times laminarizes the flow at the downstream side. Although direct numerical simulation (DNS) is a powerful tool, a lot of computations are required for assessing the influence of one roughness shape on the boundary layer. In this study, we develop an efficient method to examine a series of roughness shapes in one simulation by changing a shape parameter quasi-statically with a volume penalization (VP) method, where we should sufficiently reduce unsteady numerical noise generated at the moving shape by adjusting the moving speed and the permeability of the VP method. The subsequent change of the disturbance is observed at a downstream position, where we allow for the delay time by assuming that the disturbance takes time to be advected to this position. We demonstrate this method for optimizing discrete and sinusoidal roughness elements placed on a three-dimensional boundary layer.