Guiding-center simulations on curvilinear meshes

Jean-Philippe Braeunig 1, 2 Nicolas Crouseilles 2, 3 Michel Mehrenberger 4, 1 Eric Sonnendrücker 4, 1
1 CALVI - Scientific computation and visualization
IRMA - Institut de Recherche Mathématique Avancée, LSIIT - Laboratoire des Sciences de l'Image, de l'Informatique et de la Télédétection, Inria Nancy - Grand Est, IECL - Institut Élie Cartan de Lorraine
2 IPSO - Invariant Preserving SOlvers
IRMAR - Institut de Recherche Mathématique de Rennes, Inria Rennes – Bretagne Atlantique
Abstract : The purpose of this work is to design simulation tools for magne-tised plasmas in the ITER project framework. The specific issue we consider is the simulation of turbulent transport in the core of a Tokamak plasma, for which a 5D gyrokinetic model is generally used, where the fast gyromotion of the particles in the strong magnetic field is averaged in order to remove the associated fast timescale and to reduce the dimension of 6D phase space involved in the full Vlasov model. Very accurate schemes and efficient parallel algorithms are required to cope with these still very costly simulations. The presence of a strong magnetic field constrains the time scales of the particle motion along and accross the magnetic field line, the latter being at least an order of magnitude slower. This also has an impact on the spatial variations of the observables. Therefore, the efficiency of the algorithm can be improved considerably by aligning the mesh with the magnetic field lines. For this reason, we study the behavior of semi-Lagrangian solvers in curvilinear coordinates. Before tackling the full gyrokinetic model in a future work, we consider here the reduced 2D Guiding-Center model. We introduce our numerical algorithm and provide some numerical results showing its good properties.
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Communication dans un congrès
Numerical Models for Controlled Fusion (NMCF09), 2009, Porquerolles, France. American Institute of Mathematical Sciences, Discrete and Continuous Dynamical Systems - Series S, 5 (2), pp.271-282, 2012, 〈10.3934/dcdss.2012.5.271〉
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Jean-Philippe Braeunig, Nicolas Crouseilles, Michel Mehrenberger, Eric Sonnendrücker. Guiding-center simulations on curvilinear meshes. Numerical Models for Controlled Fusion (NMCF09), 2009, Porquerolles, France. American Institute of Mathematical Sciences, Discrete and Continuous Dynamical Systems - Series S, 5 (2), pp.271-282, 2012, 〈10.3934/dcdss.2012.5.271〉. 〈hal-01298727〉

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