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Upwind discretisation of a time-dependent two dimensional grade-two fluid model

Sujet: [MATH:MATH_NA] Mathematics/Numerical Analysis, [MATH:MATH_NA] Mathématiques/Analyse numérique, Grade-two fluid, non-linear problem, incompressible flow, time and space discretizations
Auteur: Abboud, Hyam, Sayah, Toni
Résumé: In this paper, we propose a finite-element scheme for solving numerically the equations of a transient two dimensional grade-two fluid non-Newtonian Rivlin-Ericksen fluid model. This system of equations is considered an appropriate model for the motion of a water solution of polymers. As expected, the difficulties of this problem arise from the transport equation. As one of our aims is to derive unconditional a priori estimates from the discrete analogue of the transport equation, we stabilize our scheme by adding a consistent stabilizing term. We use the P<sub>2</sub> − P<sub>1</sub> Taylor-Hood finite-element scheme for the velocity v and the pressure <i>P</i>, and the discontinuous P<sub>1</sub> finite element for an auxiliary variable z. The error is of the order of <i>h</i><sup>3/2</sup> + <i>k</i>, considering that the discretization of the transport equation loses inevitably a factor <i>h</i><sup>1/2</sup> .
Disciplines: Mathématiques
Régions: Moyen-Orient