Effective boundary conditions for compressible flows over rough boundaries

Siegfried Müller
Location
Rennes
Date and time
-
Workshop - Multiscale numerical methods for differential equations

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 e ffects. Such multiscale models rely on an appropriate
upscaling strategy. Here the strategy originally developed by Achdou et al. [1]
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 [2].
This is joint work with Giulia Deolmi and Wolfgang Dahmen.

[1] Y. Achdou, O. Pironneau, F. Valentin, Eff ective boundary conditions for laminar
flows over periodic rough boundaries, J. Comp. Phys., 147, 187--218, 1998.

[2] 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