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DTSTART;VALUE=DATE:20110405T171500
DTEND;VALUE=DATE:20110405T171500
UID:5627@agenda.unifr.ch
DESCRIPTION:A standard numerical method in order to approach the solution of a time\ndependent convection-diffusion equation in φ\ntransported with velocity <b>u</b>, consists to multiply the full equation by a space\ndependent test function ψ, to integrate it on the computational domain \nΩ and to discretize it in space with a finite element method and in\ntime with a finite difference scheme. The diffusion term is integrated by\npart on Ω but not the advected term <b>u</b>.gradφ. \n<br />\nIn the convection dominated regime, a streamline upwind method SUPG is\nused in order to stabilize the numerical scheme. In principle, when the flow\nis incompressible and confined in Ω, i.e. when div<b>u</b>=0\nin Ω and <b>u.n</b>=0 on the boundary ∂Ω, \nthe integral of φ on the domain Ω\nremains constant in time when the source term is vanishing (conservation of\nthe mass balance). However, on a practical point of view, the velocity \n<b>u</b> is often computed with a Navier-Stokes solver which leads to\nan approximation <b>u</b><sub>h</sub> which is not exactly divergence\nfree. <br />\nAs an unwelcome numerical effect, the mass balance is not conserved\nwhen the time goes up. Especially the mass balance defect can be important\nwhen the equation is integrated on a long time. In this talk, we propose an\noriginal modification of the standard numerical scheme in order to eliminate\nthis defect and we establish some error estimates produced by this scheme.<br />\n[Invited by J-P. Berrut]
SUMMARY:Prof. Dr. Jacques RAPPAZ (EPFL): About a convection-diffusion problem arising in aluminum production
CATEGORIES:Colloque / Congrès / Forum
LOCATION:PER 08\, Phys 2.52\, Chemin du Musée 3\, 1700 Fribourg
URL;VALUE=URI:https://agenda.unifr.ch/e/fr/5627
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