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Summary: European Congress on Computational Methods in Applied Sciences and Engineering
ECCOMAS 2000
Barcelona, 11-14 September 2000
c
ECCOMAS
MATHEMATICAL ANALYSIS AND FINITE ELEMENT
STRATEGY FOR 3D NUMERICAL SIMULATION OF
NAVIER STOKES EQUATIONS IN THIN DOMAINS.
Pascal AZ
ERAD
Laboratoire de Modelisation, Analyse non lineaire et Optimisation, Universite de
Perpignan, Perpignan, F-66860 cedex, France e-mail: azerad@univ-perp.fr, web page:
http://gala.univ-perp.fr/~azerad/
Key words: Numerical modelling of
ows in thin domains, hydrostatic approximation,
eddy viscosity, mixed nite element
Abstract. In this lecture, we will particularly analyze the e ect of the shallowness on
the Navier Stokes equations, together with anisotropic eddy viscosities. We will derive as
an asymptotic model the hydrostatic approximation of the Navier Stokes equations. We
will present a stable mixed 3D-FEM discretization, which allows for the computation of
the 3D-velocity as a whole. Let us emphasize that vertical velocities are not post-processed
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