Geodesic
Splitting scheme for gyro-kinetic equations with Semi-Lagrangian and Arakawa substeps
Dominik Bell1, 2 ; Martin Campos Pinto1 ; Davor Kumozec3 ; Frederik Schnack1 ; Emily Bourne4 ; Eric Sonnendrücker1, 2
1 Max-Planck-Institut für Plasmaphysik, Garching, Germany
2 Technische Universität München, Zentrum Mathematik, Garching, Germany
3 Faculty of Sciences, University of Novi Sad, Serbia
4 CEA, IRFM, Saint-Paul-les-Durance, F-13108, France
ESAIM. Proceedings, Tome 77 (2024), pp. 2-24.

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The gyro-kinetic model is an approximation of the Vlasov-Maxwell system in a strongly magnetized magnetic field. We propose a new algorithm for solving it combining the Semi-Lagrangian (SL) method and the Arakawa (AKW) scheme with a time-integrator. Both methods are successfully used in practice for different kinds of applications, in our case, we combine them by first decomposing the problem into a fast (parallel) and a slow (perpendicular) dynamical system. The SL approach and the AKW scheme will be used to solve respectively the fast and the slow subsystems. Compared to the scheme in [1], where the entire model is solved using only the SL method, our goal is to replace the method used in the slow subsystem by the AKW scheme, in order to improve the conservation of the physical constants.
DOI : 10.1051/proc/202477002

Dominik Bell 1, 2 ; Martin Campos Pinto 1 ; Davor Kumozec 3 ; Frederik Schnack 1 ; Emily Bourne 4 ; Eric Sonnendrücker 1, 2

1 Max-Planck-Institut für Plasmaphysik, Garching, Germany
2 Technische Universität München, Zentrum Mathematik, Garching, Germany
3 Faculty of Sciences, University of Novi Sad, Serbia
4 CEA, IRFM, Saint-Paul-les-Durance, F-13108, France 
@article{EP_2024_77_a1,
     author = {Dominik Bell and Martin Campos Pinto and Davor Kumozec and Frederik Schnack and Emily Bourne and Eric Sonnendr\"ucker},
     title = {Splitting scheme for gyro-kinetic equations with {Semi-Lagrangian} and {Arakawa} substeps},
     journal = {ESAIM. Proceedings},
     pages = {2--24},
     publisher = {mathdoc},
     volume = {77},
     year = {2024},
     doi = {10.1051/proc/202477002},
     language = {en},
     url = {https://geodesic-test.mathdoc.fr/articles/10.1051/proc/202477002/}
}
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Dominik Bell; Martin Campos Pinto; Davor Kumozec; Frederik Schnack; Emily Bourne; Eric Sonnendrücker. Splitting scheme for gyro-kinetic equations with Semi-Lagrangian and Arakawa substeps. ESAIM. Proceedings, Tome 77 (2024), pp. 2-24. doi : 10.1051/proc/202477002. https://geodesic-test.mathdoc.fr/articles/10.1051/proc/202477002/

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