Penalty Methods for the Hyperbolic System Modelling the Wall-Plasma Interaction in a Tokamak

  • Philippe AngotEmail author
  • Thomas Auphan
  • Olivier Guès
Conference paper
Part of the Springer Proceedings in Mathematics book series (PROM, volume 4)


The penalization method is used to take account of obstacles in a tokamak, such as the limiter. We study a non linear hyperbolic system modelling the plasma transport in the area close to the wall. A penalization which cuts the transport term of the momentum is studied. We show numerically that this penalization creates a Dirac measure at the plasma-limiter interface which prevents us from defining the transport term in the usual sense. Hence, a new penalty method is proposed for this hyperbolic system and numerical tests reveal an optimal convergence rate without any spurious boundary layer.


hyperbolic problem penalization method numerical tests 


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This work has been funded by the ANR ESPOIR (Edge Simulation of the Physics Of ITER Relevant turbulent transport)and the Fédération nationale de Recherche Fusion par Confinement Magnétique (FR-FCM). We thank Guillaume Chiavassa, Guido Ciraolo and Philippe Ghendrih for fruitful discussions.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.Laboratoire d’Analyse Topologie et Probabilités, Centre de Mathématiques et InformatiqueUniversité de ProvenceMarseille Cedex 13France

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