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Poster communications

Conservative Semi-Lagrangian solvers on mapped meshes

Michel Mehrenberger 1, 2 Morgane Bergot 1 Virginie Grandgirard 3 Guillaume Latu 3 Hocine Sellama 1 Eric Sonnendrücker 1, 2 
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
Abstract : We are interested in the numerical solution of the collisionless kinetic or gyrokinetic equations of Vlasov type needed for example for many problems in plasma physics. Different numerical methods are classically used, the most used is the Particle In Cell method, but Eulerian and Semi- Lagrangian (SL) methods that use a grid of phase space are also very interesting for some applications. Rather than using a uniform mesh of phase space which is mostly done, the structure of the solution, as a large variation of the gradients on different parts of phase space or a strong anisotropy of the solution, can sometimes be such that it is more interesting to use a more complex mesh. This is the case in particular for gyrokinetic simulations for magnetic fusion applications. We develop here a generalization of the Semi-Lagrangian method on mapped meshes. Classical Backward Semi-Lagrangian methods (BSL), Conservative Semi-Lagrangian methods based on one-dimensional splitting or Forward Semi- Lagrangian methods (FSL) have to be revisited in this case of mapped meshes. A first use of the classical advective BSL method on a mapped mesh has been described in 1. We consider here the problematic of conserving exactly some equilibrium of the distribution function, by using an adapted mapped mesh, which fits on the isolines of the Hamiltonian. This could be useful in particular for Tokamak simulations where instabilities around some equilibrium are investigated. We also consider the problem of mass conservation. In the cartesian framework, the FSL method automatically conserves the mass, as the advective and conservative form are shown to be equivalent. This does not remain true in the general curvilinear case. Numerical results are given on some gyrokinetic simulations performed with the GYSELA code and show the benefit of using a mass conservative scheme like the conservative version of the FSL scheme.
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Michel Mehrenberger, Morgane Bergot, Virginie Grandgirard, Guillaume Latu, Hocine Sellama, et al.. Conservative Semi-Lagrangian solvers on mapped meshes. ICOPS International Conference on Plasma Science, Jul 2012, Edinburgh, United Kingdom. 2012, ⟨10.1109/PLASMA.2012.6383972⟩. ⟨hal-00759823⟩



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