44 citations · 51 across the 9 of their papers we have counts for
9 papers · 1 filter
Influence of the Reynolds number on non-Newtonian flow in thin porous media
Maria Anguiano, Matthieu Bonnivard, Francisco J. Suarez-Grau
We study the effect of the Reynolds number on the flow of a generalized Newtonian fluid through a thin porous medium in . This medium is a domain of thickness $\varep…
A generalized Reynolds equation for micropolar flows past a ribbed surface with nonzero boundary conditions
Matthieu Bonnivard, Igor Pažanin, Francisco J. Suárez-Grau
Inspired by the lubrication framework, in this paper we consider a micropolar fluid flow through a rough thin domain, whose thickness is considered as the small parameter $\varepsi…
Modeling Carreau fluid flows through a very thin porous medium
María Anguiano, Matthieu Bonnivard, Francisco J. Suárez-Grau
This study investigates three-dimensional, steady-state, and non-Newtonian flows within a very thin porous medium (VTPM). The medium is modeled as a domain confined between two par…
A field-road system with a rectifiable set
Matthieu Bonnivard, Romain Ducasse, Antoine Lemenant +1
The aim of this paper is to define a field-road system in 2D where the road is a merely 1D-rectifiable set. For this purpose we introduce a general setting in order to define a par…
Asymptotic limit of linear parabolic equations with spatio-temporal degenerated potentials
Pablo Àlvarez-Caudevilla, Matthieu Bonnivard, Antoine Lemenant
In this paper, we observe how the heat equation in a non-cylindrical domain can arise as the asymptotic limit of a parabolic problem in a cylindrical domain, by adding a potential…
Effective models for generalized Newtonian fluids through a thin porous medium following the Carreau law
Maria Anguiano, Matthieu Bonnivard, Francisco Javier Suarez-Grau
We consider the flow of a generalized Newtonian fluid through a thin porous medium of thickness , perforated by periodically distributed solid cylinders of size . We assume t…
On the instability of travelling wave solutions for the transport-Stokes equation
Matthieu Bonnivard, Amina Mecherbet
In this paper, we investigate the instability of the spherical travelling wave solutions for the Transport-Stokes system in . First, a classical scaling argument ensu…
On a phase field approximation of the planar Steiner problem: existence, regularity, and asymptotic of minimizers
Matthieu Bonnivard, Antoine Lemenant, Vincent Millot
In this article, we consider and analyse a small variant of a functional originally introduced in \cite{BLS,LS} to approximate the (geometric) planar Steiner problem. This function…
Computation of the effective slip of rough hydrophobic surfaces via homogenization
Matthieu Bonnivard, Anne-Laure Dalibard, David Gérard-Varet
We present a quantitative analysis of the effect of rough hydrophobic surfaces on viscous newtonian flows. We use a model introduced by Ybert and coauthors in which the rough surfa…