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Effective Boundary Conditions: A General Strategy and Application to Compressible Flows over Rough Boundaries

Effective Boundary Conditions: A General Strategy and Application to Compressible Flows over Rough Boundaries
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Year:    2017

Author:    Giulia Deolmi, Wolfgang Dahmen, Siegfried Müller

Communications in Computational Physics, Vol. 21 (2017), Iss. 2 : pp. 358–400

Abstract

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 "smooth" means the absence of any micro-scale roughness. Our derivation is based on a "conceptual recipe" 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.
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 "micro-scale size" 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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.OA-2016-0015

Communications in Computational Physics, Vol. 21 (2017), Iss. 2 : pp. 358–400

Published online:    2017-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    43

Keywords:   

Author Details

Giulia Deolmi

Wolfgang Dahmen

Siegfried Müller

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  11. Elucidating the impact of micro-scale heterogeneous bacterial distribution on biodegradation

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  12. A reduced order model to simulate compressible flows over an actuated riblet surface

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

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