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Preprint-No.: <   443   >   Published in: January 2016   PDF-File: IGPM443.pdf
Title:Effective boundary conditions: a general strategy and application to compressible flows over rough boundaries
Authors:Giulia Deolmi, Wolfgang Dahmen, Siegfried Müller
Determining the drag of a flow over a rough surface is a guiding example for the need to take geometric micro-scale effects into account when computing a macro-scale quantity. A well-known strategy to avoid a prohibitively expensive numerical resolution of micro-scale structures is to capture the micro-scale effects through some effective boundary conditions posed for a problem on a (virtually) smooth domain. The central objective of this paper is to propose a “conceptual recipe” for the derivation of such effective boundary conditions first in a general setting of boundary value problems under the assumption of sufficient regularity to permit asymptotic expansions in terms of the micro-scale parameter. The proposed multiscale model relies then on an upscaling strategy based on homogenization techniques. It is similar in spirit to previous works by Achdou et al. [1], Jäger and Mikelic [29, 31], Friedmann et al. [24, 25] for incompressible fluids and Deolmi et al. [16, 17] for compressible fluids although with several noteworthy distinctions regarding e.g. the “micro-scale size” relative to boundary layer thickness or the systematic treatment of different boundary conditions. For proof of concept the general strategy is applied to the compressible Navier-Stokes equations to investigate steady, laminar, subsonic flow over a flat plate with partially embedded isotropic and anisotropic periodic roughness imposing adiabatic and isothermal wall conditions, respectively. The results are compared with high resolution simulations on a fully resolved rough domain.
Keywords:homogenization, upscaling strategy, effective boundary conditions, Navier wall law, compressible flow
DOI: 10.4208/cicp.OA-2016-0015
Publication:Communications in computational physics
CiCP 21(2), 358-400 (2017)
Corresponding author:Siegfried Müller