A two-step model order reduction method to simulate a compressible flow over an extended rough surface

In this paper the ideas presented in the article Deolmi et al. (2017) to simulate efficiently a compressible flow over a rough surface are extended to a two-step model order reduction strategy. The first level consists in the formulation of effective boundary conditions, to take into account the effect of the roughness without resolving it. This requires the solution of a parameter-dependent cell problem on the micro-scale. To reduce its computational cost we add an additional step, where a second level of reduction is applied to the cell problem by means of the reduced basis method. Through numerical computations we verify the gain in efficiency of this strategy.