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

Hyam Abboud (1) , Toni Sayah (2)

1 USEK - Université Saint-Esprit de Kaslik
2 FS - Faculté des sciences-USJ

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 P₂ − P₁ Taylor-Hood finite-element scheme for the velocity v and the pressure P, and the discontinuous P₁ finite element for an auxiliary variable z. The error is of the order of h^3/2 + k, considering that the discretization of the transport equation loses inevitably a factor h^1/2 .

Mots clés: Grade-two fluid; non-linear problem; incompressible flow; time and space discretizations.; time and space discretizations

Domaines: Analyse numérique [math.NA]

Hyam Abboud, Toni Sayah. Upwind discretisation of a time-dependent two dimensional grade-two fluid model. 2007. ⟨hal-00141016⟩