Mathematical modeling and numerical computation of the effective interfacial conditions for Stokes flow on an arbitrarily rough solid surface

doi:10.1007/s10483-021-2733-9

Applied Mathematics and Mechanics (English Edition) ›› 2021, Vol. 42 ›› Issue (5): 721-746.doi: https://doi.org/10.1007/s10483-021-2733-9

Mathematical modeling and numerical computation of the effective interfacial conditions for Stokes flow on an arbitrarily rough solid surface

A. T. TRAN¹, H. LE QUANG², Q. C. HE^2,3, D. H. NGUYEN¹

1. Research and Application Center for Technology in Civil Engineering, University of Transport and Communications, Hanoi 10000, Vietnam;
2. Laboratoire Modélisation et Simulation Multi-Echelle, Unité Mixte de Recherche 8208, Centre National de la Recherche Scientifique, Université Gustave Eiffel, Marne-la-Vallée F-77454, France;
3. School of Mechanical Engineering, Southwest Jiaotong University, Chengdu 610031, China

收稿日期:2020-07-16 修回日期:2021-03-12 出版日期:2021-05-01 发布日期:2021-04-22
通讯作者: H. LE QUANG, E-mail:hung.lequang@univ-paris-est.fr
基金资助:
the Vietnam National Foundation for Science and Technology Development (NAFOSTED) (No. 107.02-2017.310)

Mathematical modeling and numerical computation of the effective interfacial conditions for Stokes flow on an arbitrarily rough solid surface

A. T. TRAN¹, H. LE QUANG², Q. C. HE^2,3, D. H. NGUYEN¹

1. Research and Application Center for Technology in Civil Engineering, University of Transport and Communications, Hanoi 10000, Vietnam;
2. Laboratoire Modélisation et Simulation Multi-Echelle, Unité Mixte de Recherche 8208, Centre National de la Recherche Scientifique, Université Gustave Eiffel, Marne-la-Vallée F-77454, France;
3. School of Mechanical Engineering, Southwest Jiaotong University, Chengdu 610031, China

Received:2020-07-16 Revised:2021-03-12 Online:2021-05-01 Published:2021-04-22
Contact: H. LE QUANG, E-mail:hung.lequang@univ-paris-est.fr
Supported by:
the Vietnam National Foundation for Science and Technology Development (NAFOSTED) (No. 107.02-2017.310)

摘要/Abstract

摘要： The present work is concerned with a two-dimensional (2D) Stokes flow through a channel bounded by two parallel solid walls. The distance between the walls may be arbitrary, and the surface of one of the walls can be arbitrarily rough. The main objective of this work consists in homogenizing the heterogeneous interface between the rough wall and fluid so as to obtain an equivalent smooth slippery fluid/solid interface characterized by an effective slip length. To solve the corresponding problem, two efficient numerical approaches are elaborated on the basis of the method of fundamental solution (MFS) and the boundary element methods (BEMs). They are applied to different cases where the fluid/solid interface is periodically or randomly rough. The results obtained by the proposed two methods are compared with those given by the finite element method and some relevant ones reported in the literature. This comparison shows that the two proposed methods are particularly efficient and accurate.

关键词: effective slip length, method of fundamental solution (MFS), boundary element method (BEM), Stokeslet, micro-channel, fluid/solid interface

Abstract: The present work is concerned with a two-dimensional (2D) Stokes flow through a channel bounded by two parallel solid walls. The distance between the walls may be arbitrary, and the surface of one of the walls can be arbitrarily rough. The main objective of this work consists in homogenizing the heterogeneous interface between the rough wall and fluid so as to obtain an equivalent smooth slippery fluid/solid interface characterized by an effective slip length. To solve the corresponding problem, two efficient numerical approaches are elaborated on the basis of the method of fundamental solution (MFS) and the boundary element methods (BEMs). They are applied to different cases where the fluid/solid interface is periodically or randomly rough. The results obtained by the proposed two methods are compared with those given by the finite element method and some relevant ones reported in the literature. This comparison shows that the two proposed methods are particularly efficient and accurate.

Key words: effective slip length, method of fundamental solution (MFS), boundary element method (BEM), Stokeslet, micro-channel, fluid/solid interface

中图分类号:

74Q15

A. T. TRAN, H. LE QUANG, Q. C. HE, D. H. NGUYEN. Mathematical modeling and numerical computation of the effective interfacial conditions for Stokes flow on an arbitrarily rough solid surface[J]. Applied Mathematics and Mechanics (English Edition), 2021, 42(5): 721-746.

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Mathematical modeling and numerical computation of the effective interfacial conditions for Stokes flow on an arbitrarily rough solid surface

Mathematical modeling and numerical computation of the effective interfacial conditions for Stokes flow on an arbitrarily rough solid surface

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