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Mathematical properties of hierarchies of reduced MHD models
Post-edited
Authors : Després, Bruno (Author of the conference)
CIRM (Publisher )
35L65 - Conservation laws
35Q30 - Stokes and Navier-Stokes equations
65M60 - Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (IVP of PDE)
76W05 - Magnetohydrodynamics and electrohydrodynamics
CIRM (Publisher )
Abstract :
Reduced MHD models in Tokamak geometry are convenient simplifications of full MHD and are fundamental for the numerical simulation of MHD stability in Tokamaks. This presentation will address the mathematical well-posedness and the justification of the such models.
The first result is a systematic design of hierachies of well-posed reduced MHD models. Here well-posed means that the system is endowed with a physically sound energy identity and that existence of a weak solution can be proved. Some of these models will be detailed.
The second result is perhaps more important for applications. It provides understanding on the fact the the growth rate of linear instabilities of the initial (non reduced) model is lower bounded by the growth rate of linear instabilities of the reduced model.
This work has been done with Rémy Sart.
MSC Codes : The first result is a systematic design of hierachies of well-posed reduced MHD models. Here well-posed means that the system is endowed with a physically sound energy identity and that existence of a weak solution can be proved. Some of these models will be detailed.
The second result is perhaps more important for applications. It provides understanding on the fact the the growth rate of linear instabilities of the initial (non reduced) model is lower bounded by the growth rate of linear instabilities of the reduced model.
This work has been done with Rémy Sart.
35L65 - Conservation laws
35Q30 - Stokes and Navier-Stokes equations
65M60 - Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (IVP of PDE)
76W05 - Magnetohydrodynamics and electrohydrodynamics
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 26/08/14 Conference Date : 01/08/14 Subseries : Research talks arXiv category : Numerical Analysis ; Mathematical Physics Mathematical Area(s) : PDE ; Numerical Analysis & Scientific Computing ; Mathematical Physics Format : QuickTime (.mov) Video Time : 01:03:04 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2014-08-01_Despres.mp4 
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Information on the Event
Event Title : CEMRACS : Numerical modeling of plasmas / CEMRACS : Modèles numériques des plasmasEvent Organizers : Campos Pinto, Martin ; Charles, Frédérique ; Guillard, Hervé ; Nkonga, Boniface Dates : 21/07/14 - 29/08/14 Event Year : 2014 Event URL : http://smai.emath.fr/cemracs/cemracs14/
Citation Data
DOI : 10.24350/CIRM.V.18557303Cite this video as: Després, Bruno (2014). Mathematical properties of hierarchies of reduced MHD models. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.18557303 URI : http://dx.doi.org/10.24350/CIRM.V.18557303 |
Bibliography
- Després, B., Sart, R. Navier-Stokes hierarchies of reduced MHD models in Tokamak geometry. Hal preprint - http://hal.archives-ouvertes.fr/hal-00796425
- Després, B., Sart, R. Reduced resistive MHD in Tokamaks with general density. ESAIM: Mathematical Modelling and Numerical Analysis 46 (2012) no. 5, pp 1081-1106 - http://dx.doi.org/10.1051/m2an/2011078
