The derivation of a nonlinear filtration law including the inertia effects via homogenization
type: Item
instance of: scholarly article
title: The derivation of a nonlinear filtration law including the inertia effects via homogenization
zbMATH Open document ID: 0965.35131
DOI: 10.1016/S0362-546X(98)00346-0
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2001-07-19T00:00:00Z
review text: The authors develop a nonlinear relationship between the pressure gradient and the filtration velocity starting from the stationary incompressible Navier-Stokes equations in a periodic porous medium. Considering that the local Reynolds number is of order 1 (in this case the inertial terms are not negligible) and performing the formal asymptotic expansion with respect to a small parameter representing the ratio between the microscopic length scale and the macroscopic characteristic length, they replace the non-dimensional incompressible Navier-Stokes system with a homogenized problem for which they give existence and uniqueness results. According to the constitutive law found out by the authors, the filtration velocity is a nonlinear function depending on the external force and pressure gradient. After establishing the analyticity of the nonlinear function in a ball around zero, the authors prove that for some values of the Reynolds number, it is possible to approximate the nonlinear filtration law by a quadratic law. Finally, the proof of the convergence of the homogeneization process justifies rigorously the nonlinear filtration law.
reviewed by: Adrian Carabineanu
Mathematics Subject Classification ID: 35Q35
Mathematics Subject Classification ID: 76S05
Mathematics Subject Classification ID: 76M50
zbMATH DE Number: 1491641
zbMATH Keywords: existence
zbMATH Keywords: uniqueness
zbMATH Keywords: nonlinear filtration law
zbMATH Keywords: porous medium
zbMATH Keywords: Navier-Stokes system
author: Eduard Marušić-Paloka
author: Andro Mikelić
MaRDI profile type: Publication
full work available at URL: s0362-546x(98)00346-0
OpenAlex ID: W2007185010
description: scientific article; zbMATH DE number 1491641