@Article{CiCP-21-358,
author = {Deolmi , GiuliaDahmen , Wolfgang and Müller , Siegfried},
title = {Effective Boundary Conditions: A General Strategy and Application to Compressible Flows over Rough Boundaries},
journal = {Communications in Computational Physics},
year = {2018},
volume = {21},
number = {2},
pages = {358--400},
abstract = {<p style="text-align: justify;">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 develop a numerical scheme for accurately capturing
the micro-scale effects at essentially the cost of twice solving a problem on a
(piecewise) smooth domain at affordable resolution. Here and throughout the paper
&quot;smooth&quot; means the absence of any micro-scale roughness. Our derivation is based
on a &quot;conceptual recipe&quot; formulated first in a simplified setting of boundary value
problems under the assumption of sufficient local regularity to permit asymptotic expansions
in terms of the micro-scale parameter.<br/>The proposed multiscale model relies then on an upscaling strategy similar in
spirit to previous works by Achdou et al. [1], Jäger and Mikelic [29, 31], Friedmann
et al. [24, 25], for incompressible fluids. Extensions to compressible fluids, although with
several noteworthy distinctions regarding e.g. the &quot;micro-scale size&quot; relative to boundary
layer thickness or the systematic treatment of different boundary conditions, are
discussed in Deolmi et al. [16,17]. 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 direct simulations on a fully resolved rough domain.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2016-0015},
url = {http://global-sci.org/intro/article_detail/cicp/11242.html}
}