arXiv subjects

Alain Brillard

Publications and source records attributed to Alain Brillard.

3 recordsLinked to original sources

arXiv2010

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. As a further application, we consider an optimal control problem within this context.

math.AP↗

arXiv2010

Asymptotic analysis of pollution filtration through thin random fissures between two porous media

We describe the asymptotic behaviour of a filtration problem from a contaminated porous medium to a non-contaminated porous medium through thin vertical fissures of fixed height h>0, of random thinness of order ε and which are $ε$-periodically distributed. We compute the limit velocity of the flow and the limit flux of pollutant at the interfaces between the two porous media and the intermediate one.

math.AP↗

arXiv2010

Asymptotic behaviour of a cylindrical elastic structure periodically reinforced along identical fibers

We describe the asymptotic behaviour of a cylindrical elastic body, reinforced along identical $ε$-periodically distributed fibers of size $r_ε$, with $0 < r_ε < ε$, filled in with some different elastic material, when this small parameter $ε$ goes to 0. The case of small deformations and small strains is considered. We exhibit a critical size of the fibers and a critical link between the radius of the fibers and the size of the Lamé coefficients of the reinforcing elastic material. Epi-convergence arguments are used in order to prove this asymptotic behaviour. The proof is essentially based on the construction of appropriate test-functions.

math.AP↗