Eric Sonnendrücker

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The presence of a large external magnetic field in a plasma introduces an additional time-scale which is very constraining for the numerical simulation. Hence it is very useful to introduce averaged models which remove this time-scale. However, depending on other parameters of the plasma, different starting models for the asymptotic analysis may be(More)
Conservative Numerical Schemes for the Vlasov Equation Francis Filbet,∗ Eric Sonnendrücker,† and Pierre Bertrand‡ ∗IECN–INRIA Project Numath, Université de Nancy I, BP 239, 54506 Vandœuvre-lès-Nancy Cedex, France; †IRMA, Université Louis Pasteur, 7 Rue R Descartes, 67084 Strasbourg, France; and ‡LPMI, Université de Nancy I, BP 239, 54506 Vandœuvre-lès-Nancy(More)
Abstract: Motivated by the difficulty arising in the numerical simulation of the movement of charged particles in presence of a large external magnetic field, which adds an additional time scale and thus imposes to use a much smaller time step, we perform in this paper a homogenization of the Vlasov equation and the Vlasov-Poisson system which yield(More)
Conservative methods for the numerical solution of the Vlasov equation are developed in the context of the one-dimensional splitting. In the case of constant advection, these methods and the traditional semi-Lagrangian ones are proven to be equivalent, but the conservative methods offer the possibility to add adequate filters in order to ensure the(More)
We study the two-scale asymptotics for a charged beam under the action of a rapidly oscillating external electric field. After proving the convergence to the correct asymptotic state, we develop a numerical method for solving the limit model involving two time scales and validate its efficiency for the simulation of long time beam evolution.
A new code is presented here, named Gyrokinetic SEmi-LAgragian (GYSELA) code, which solves 4D drift-kinetic equations for ion temperature gradient driven turbulence in a cylinder (r,h,z). The code validation is performed with the slab ITG mode that only depends on the parallel velocity. This code uses a semi-Lagrangian numerical scheme, which exhibits good(More)
This paper deals with the numerical simulations of the Vlasov-Poisson equation using a phase space grid in the quasi-neutral regime. In this limit, explicit numerical schemes suffer from numerical constraints related to the small Debye length and large plasma frequency. Here, we propose a semi-Lagrangian scheme for the Vlasov-Poisson model in the(More)
This work deals with the numerical solution of the Vlasov equation. This equation gives a kinetic description of the evolution of a plasma, and is coupled with Poisson’s equation for the computation of the self-consistent electric field. The coupled model is non linear. A new semi-Lagrangian method, based on forward integration of the characteristics, is(More)