arXiv subjects

Makram Hamouda

Publications and source records attributed to Makram Hamouda.

21 records · Page 2Linked to original sources

arXiv2016

New Finite Volume Method for rotating channel flows involving boundary layers

We investigate in this article the boundary layers appearing for a fluid under moderate rotation when the viscosity is small. The fluid is modeled by rotating type Stokes equations known also as the Barotropric mode equations in the primitive equations theory. First we derive the correctors that describe the sharp variations at large Reynolds number (i.e., small viscosity). Second, thanks to a new finite volume method (NFVM) we give numerical solutions of the rotating Stokes system at small viscosity. The NFVM can be applied to a large class of singular perturbation problems.

math.AP↗

arXiv2015

Numerical solutions for a Timoshenko-type system with thermoelasticity with second sound

In this work, we consider a nonlinear vibrating Timoshenko system with thermoelasticity with second sound. We recall first the results of well-posdness and regularity and the asymptotic behavior of the energy obtained in \cite{Ayadi}. Then, we use a fourth order finite difference scheme to compute the numerical solutions and thus we show the energy decay in several cases depending on the stability number. Résumé : Dans ce travail, on considère le système de Timoshenko non-linéaire avec Thermo-élasticité et deuxième son. On rappelle d'abord les résultats d'existence, de régularité et du comportement asymptotique de l'énergie obtenus dans \cite{Ayadi}. Ensuite, on valide numériquement ces résultats théoriques. Pour cela, on utilise une méthode de différences finies d'ordre $4$. Ainsi la solution numérique obtenue permet de valider la décroissance de l'énergie dans plusieurs cas selon la valeur du paramètre de stabilité.

math.NA↗

arXiv2015

Very weak solutions of the Stokes problem in a convex polygon

Motivated by the study of the corner singularities in the so-called cavity flow, we establish in this article, the existence and uniqueness of solutions in $L^2(Ω)^2$ for the Stokes problem in a domain $Ω,$ when $Ω$ is a smooth domain or a convex polygon. We establish also a trace theorem and show that the trace of $u$ can be arbitrary in $L^2(\partialΩ)^2.$ The results are also extended to the linear evolution Stokes problem.

math.AP↗