A standard numerical method in order to approach the solution of a time

dependent convection-diffusion equation in φ

transported with velocity **u**, consists to multiply the full equation by a space

dependent test function ψ, to integrate it on the computational domain

Ω and to discretize it in space with a finite element method and in

time with a finite difference scheme. The diffusion term is integrated by

part on Ω but not the advected term **u**.gradφ.

In the convection dominated regime, a streamline upwind method SUPG is

used in order to stabilize the numerical scheme. In principle, when the flow

is incompressible and confined in Ω, i.e. when div**u**=0

in Ω and **u.n**=0 on the boundary ∂Ω,

the integral of φ on the domain Ω

remains constant in time when the source term is vanishing (conservation of

the mass balance). However, on a practical point of view, the velocity
**u** is often computed with a Navier-Stokes solver which leads to

an approximation **u**_{h} which is not exactly divergence

free.

As an unwelcome numerical effect, the mass balance is not conserved

when the time goes up. Especially the mass balance defect can be important

when the equation is integrated on a long time. In this talk, we propose an

original modification of the standard numerical scheme in order to eliminate

this defect and we establish some error estimates produced by this scheme.

[Invited by J-P. Berrut]

When? | 05.04.2011 17:15 |
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Where? | PER 08 Phys 2.52 Chemin du Musée 3 1700 Fribourg |

Contact | Department of Mathematics isabella.schmutz@unifr.ch |