Finite Element Solution for the Generalized Stokes Problem in axisymmetric geometry
A. Elamari1*, H. Sammouda2, A. Belghith1
1LETTM, Department of Physics Faculty of Sciences of Tunis 1060 Tunis, Tunisia
2LETTM, Department of Physics Faculty of Sciences of Monastir 5019 Monastir, Tunisia
* Corresponding author . E-mail : Adel.ElAmari@fst.rnu.tn
Received : 06 June 2003; revised version accepted : 04 April 2004
This study develops an iterative solver for the unsteady axisymmetric Stokes equations in primitive variables in cylindrical geometries. The motivation of this method relies on the analysis of a class of fractional-step methods for the Navier-Stokes equations. This solver is based on the finite element method and on an approximation of the preconditioned Uzawa scheme. A new class of interpolation functions, and a new preconditioner are introduced to ensure the convergence and the stability of the numerical scheme. The validation of this model is gotten by the simulation of the unsteady incompressible axisymmetric flow in a lid-driven cavity with smooth boundary conditions. A sensible comparison is made with the numerical experiments data for different values of Reynolds number through which we have proved the quality of this solver. The convergence analysis proves the stability and the satisfaction of inf-sup condition by the velocity-pressure interpolation in axisymmetric geometries.
Keywords: Axisymmetric geometry; Finite element method; Generalized Stokes Problem; Primitive variables; Uzawa scheme; Driven cavity