Simulations of a flow over a roughness are prohibitively expensive for small scale structures.
If the interest is only on some macroscale quantity it will be sufficient to model
the in fluence of the unresolved microscale effects. Such multiscale models rely on an appropriate
upscaling strategy. Here the strategy originally developed by Achdou et al. 
for incompressible flows is extended to compressible high-Reynolds number flow. For
proof of concept a laminar flow over a fl at plate with partially embedded roughness is
simulated. The results are compared with computations on a rough domain. They have been published recently in .
This is joint work with Giulia Deolmi and Wolfgang Dahmen.
 Y. Achdou, O. Pironneau, F. Valentin, Effective boundary conditions for laminar
flows over periodic rough boundaries, J. Comp. Phys., 147, 187--218, 1998.
 Effective boundary conditions for compressible flows over rough boundaries
Giulia Deolmi, Wolfgang Dahmen, and Siegfried Müller
Mathematical Models and Methods in Applied Sciences 2015 25:07, 1257-1297