Asymptotic analysis of the laminar viscous flow over a porous bed

Jäger W, Mikelic A, Neuß N (2001)

Publication Language: English

Publication Type: Journal article, Original article

Publication year: 2001

Journal

SIAM Journal on Computing Society for Industrial and Applied Mathematics

Book Volume: 22,6

Pages Range: 2006--2028

DOI: 10.1137/S1064827599360339

Abstract

We consider the laminar viscous channel flow over a porous surface. The size of the pores is much smaller than the size of the channel and it is important to determine the effective boundary conditions at the porous surface.  We study the corresponding boundary layers, and, by a rigorous asymptotic expansion, we obtain Saffman's modification of the interface condition observed by Beavers and Joseph. The effective coefficient in the law is determined through an auxiliary boundary-layer type problem, whose computational and modeling aspects are discussed in detail. Furthermore, the approximation errors for the velocity and for the effective mass flow are given as powers of the characteristic pore size $\eps$. Finally, we give the interface condition linking the effective pressure fields in the porous medium and in the channel, and determine the jump of the effective pressures explicitly.

Authors with CRIS profile

Nicolas Neuß Lehrstuhl für Angewandte Mathematik (Wissenschaftliches Rechnen)

Involved external institutions

Ruprecht-Karls-Universität Heidelberg DE Germany (DE) Université Claude Bernard Lyon 1 (UCB) FR France (FR)

How to cite

APA:

Jäger, W., Mikelic, A., & Neuß, N. (2001). Asymptotic analysis of the laminar viscous flow over a porous bed. SIAM Journal on Computing, 22,6, 2006--2028. https://doi.org/10.1137/S1064827599360339

MLA:

Jäger, Willi, Andro Mikelic, and Nicolas Neuß. "Asymptotic analysis of the laminar viscous flow over a porous bed." SIAM Journal on Computing 22,6 (2001): 2006--2028.

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