Analysis of localized damping effects in channel flows with a periodic rough boundary

Jaewook Ahn; Jung Il Choi; Kyungkeun Kang; Jihye Lim

doi:10.1080/00036811.2017.1293818

Analysis of localized damping effects in channel flows with a periodic rough boundary

Jaewook Ahn, Jung Il Choi, Kyungkeun Kang, Jihye Lim

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

In this study, we justify a modified stationary Navier–Stokes system involving the damping effect for a channel flow with periodic roughness. We solve the modified Navier–Stokes system in a smooth extended channel after reducing the rough boundary to a parameter in a linear damping term. We find that the proposed damping term is valid when the size and amplitude of the imperfection tend to zero. Furthermore, the term yields an O(ε^3/2) quadratic approximation of real flow, i.e. O(ε^3/2) approximation in the L²-norm, for a small pressure difference. An effective mass flow is also determined up to an order of O(ε^3/2).

Original language	English
Pages (from-to)	902-918
Number of pages	17
Journal	Applicable Analysis
Volume	97
Issue number	6
DOIs	https://doi.org/10.1080/00036811.2017.1293818
Publication status	Published - 2018 Apr 26

Bibliographical note

Funding Information:
This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korean government (MSIP) [grant number NRF-20151009350] and in part by the Yonsei University Future-leading Research Initiative of 2014.

Funding Information:
This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korean government (MSIP) [grant number NRF-20151009350] and in part by the Yonsei Universityuture-leading Research Initiative of 2014.

Publisher Copyright:
© 2017 Informa UK Limited, trading as Taylor & Francis Group.

All Science Journal Classification (ASJC) codes

Analysis
Applied Mathematics

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10.1080/00036811.2017.1293818

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title = "Analysis of localized damping effects in channel flows with a periodic rough boundary",

abstract = "In this study, we justify a modified stationary Navier–Stokes system involving the damping effect for a channel flow with periodic roughness. We solve the modified Navier–Stokes system in a smooth extended channel after reducing the rough boundary to a parameter in a linear damping term. We find that the proposed damping term is valid when the size and amplitude of the imperfection tend to zero. Furthermore, the term yields an O(ε3/2) quadratic approximation of real flow, i.e. O(ε3/2) approximation in the L2-norm, for a small pressure difference. An effective mass flow is also determined up to an order of O(ε3/2).",

author = "Jaewook Ahn and Choi, {Jung Il} and Kyungkeun Kang and Jihye Lim",

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AU - Ahn, Jaewook

AU - Choi, Jung Il

AU - Kang, Kyungkeun

AU - Lim, Jihye

N1 - Funding Information: This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korean government (MSIP) [grant number NRF-20151009350] and in part by the Yonsei University Future-leading Research Initiative of 2014. Funding Information: This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korean government (MSIP) [grant number NRF-20151009350] and in part by the Yonsei Universityuture-leading Research Initiative of 2014. Publisher Copyright: © 2017 Informa UK Limited, trading as Taylor & Francis Group.

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N2 - In this study, we justify a modified stationary Navier–Stokes system involving the damping effect for a channel flow with periodic roughness. We solve the modified Navier–Stokes system in a smooth extended channel after reducing the rough boundary to a parameter in a linear damping term. We find that the proposed damping term is valid when the size and amplitude of the imperfection tend to zero. Furthermore, the term yields an O(ε3/2) quadratic approximation of real flow, i.e. O(ε3/2) approximation in the L2-norm, for a small pressure difference. An effective mass flow is also determined up to an order of O(ε3/2).

AB - In this study, we justify a modified stationary Navier–Stokes system involving the damping effect for a channel flow with periodic roughness. We solve the modified Navier–Stokes system in a smooth extended channel after reducing the rough boundary to a parameter in a linear damping term. We find that the proposed damping term is valid when the size and amplitude of the imperfection tend to zero. Furthermore, the term yields an O(ε3/2) quadratic approximation of real flow, i.e. O(ε3/2) approximation in the L2-norm, for a small pressure difference. An effective mass flow is also determined up to an order of O(ε3/2).

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Analysis of localized damping effects in channel flows with a periodic rough boundary

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