Geodesic
Anisotropic Diffusion in Toroidal geometries
Ahmed Ratnani1 ; Emmanuel Franck2 ; Boniface Nkonga3 ; Alina Eksaeva4 ; Maria Kazakova5
1Max-Planck Institute für PlasmaPhysik, Garching, Munich
2Inria Nancy Grand-Est & IRMA, Strasbourg, France
3Laboratoire Jean Dieudonné, Université Nice Sophia-Antipolis, Nice, France
4Moscow Engineering & Physics Institute MEPHI, Russia
5Lavrentyev Institute of Hydrodynamics of SB RAS, Russia
ESAIM. Proceedings, Tome 53 (2016), pp. 77-98
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In this work, we present a new finite element framework for toroidal geometries based on a tensor product description of the 3D basis functions. In the poloidal plan, different discretizations, including B-splines and cubic Hermite-Bézier surfaces are defined, while for the toroidal direction both Fourier discretization and cubic Hermite-Bézier elements can be used. In this work, we study the MHD equilibrium by solving the Grad-Shafranov equation, which is the basis and the starting point of any MHD simulation. Then we study the anisotropic diffusion problem in both steady and unsteady states.
DOI : 10.1051/proc/201653006

Ahmed Ratnani  1   ; Emmanuel Franck  2   ; Boniface Nkonga  3   ; Alina Eksaeva  4   ; Maria Kazakova  5

1 Max-Planck Institute für PlasmaPhysik, Garching, Munich
2 Inria Nancy Grand-Est & IRMA, Strasbourg, France
3 Laboratoire Jean Dieudonné, Université Nice Sophia-Antipolis, Nice, France
4 Moscow Engineering & Physics Institute MEPHI, Russia
5 Lavrentyev Institute of Hydrodynamics of SB RAS, Russia 
@article{EP_2016_53_a6,
     author = {Ahmed Ratnani and Emmanuel Franck and Boniface Nkonga and Alina Eksaeva and Maria Kazakova},
     title = {Anisotropic {Diffusion} in {Toroidal} geometries},
     journal = {ESAIM. Proceedings},
     pages = {77--98},
     year = {2016},
     volume = {53},
     doi = {10.1051/proc/201653006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/201653006/}
}
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Ahmed Ratnani; Emmanuel Franck; Boniface Nkonga; Alina Eksaeva; Maria Kazakova. Anisotropic Diffusion in Toroidal geometries. ESAIM. Proceedings, Tome 53 (2016), pp. 77-98. doi: 10.1051/proc/201653006

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