Wall laws for fluid flows at a boundary with random roughness

The Navier wall law at a boundary with random roughness

We consider the Navier-Stokes equation in a domain with irregular boundaries. The irregularity is modeled by a spatially homogeneous random process, with typical size $\eps \ll 1$. In a parent paper, we derived a homogenized boundary condition of Navier type as $\eps \to 0$. We show here that for a large class of boundaries, this Navier condition provides a $O(\eps^{3/2} |\ln \eps|^{1/2})$ approximation in $L^2$, instead of $O(\eps^{3/2})$ for periodic irregularities. Our result relies on the study of an auxiliary boundary layer system. Decay properties of this boundary layer are deduced from …

Computation of the drag force on a rough sphere close to a wall

We consider the effect of surface roughness on solid-solid contact in a Stokes flow. Various models for the roughness are considered, and a unified methodology is given to derive the corresponding asymptotics of the drag force. In this way, we recover and clarify the various expressions that can be found in the litterature.

High Order Multi-Scale Wall-Laws, Part I : The Periodic Case

In this work we present new wall-laws boundary conditions including microscopic oscillations. We consider a newtonian flow in domains with periodic rough boundaries that we simplify considering a Laplace operator with periodic inflow and outflow boundary conditions. Following the previous approaches, see [A. Mikelic, W. Jäger, J. Diff. Eqs, 170, 96-122, (2001) ] and [Y. Achdou, O. Pironneau, F. Valentin, J. Comput. Phys, 147, 1, 187-218, (1998)], we construct high order boundary layer approximations and rigorously justify their rates of convergence with respect to epsilon (the roughness' thick…

粗糙度诱导的热微极流体在薄域中的流动效应

Roughness-induced effects on the thermomicropolar fluid flow through a thin domain

本文研究了粗糙边界薄通道中热微极流体流动的渐近行为，通过推导不同渐近模型揭示粗糙度对平均速度和微旋转的影响。

Effective wall-laws for the Stokes equations over curved rough boundaries

We derive effective wall-laws for Stokes systems with inhomogeneous boundary conditions in three dimensional bounded domains with curved rough boundaries. No-slip boundary condition is given on the locally periodic rough boundary parts with characteristic roughness size $ε$ and boundary data is assumed to be supported in the nonoscillatory smooth boundary. Based on the analysis of a boundary layer cell problem depending on geometry of the fictitious boundary and roughness shape, boundary layer approximations are constructed using orthogonal tangential vectors and normal vector on the fictitiou…

Boundary Asymptotic Analysis for an Incompressible Viscous Flow: Navier Wall Laws

We consider a new way of establishing Navier wall laws. Considering a bounded domain $Ω$ of R N , N=2,3, surrounded by a thin layer $Σε$, along a part $Γ$2 of its boundary $\partial Ω$, we consider a Navier-Stokes flow in $Ω\cup \partial Ω\cup Σε$ with Reynolds' number of order 1/$ε$ in $Σε$. Using $Γ$-convergence arguments, we describe the asymptotic behaviour of the solution of this problem and get a general Navier law involving a matrix of Borel measures having the same support contained in the interface $Γ$2. We then consider two special cases where we characterize this matrix of measures.…