Eric Sonnendrücker

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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)
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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 approximate(More)
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(More)
We introduce here a new method for the numerical resolution of the Vlasov equation on a phase space grid using an adaptive semi-Lagrangian method. The adaptiv-ity is obtained through a multiresolution analysis which enables to keep or remove grid points from the simulation depending on the size of their associated coefficients in a multiresolution(More)
Vlasov simulations can for some situations be a valuable alternative to PIC simulations for the study of intense beam propagation. However, as they rely on a phase-space grid which is fixed for the whole simulation, important computing effort can be wasted in zones where no particles are present at some given time. In order to overcome this drawback, we(More)
A method for computing the numerical solution of Vlasov type equations on massively parallel computers is presented. In contrast with Particle In Cell methods which are known to be noisy, the method is based on a semi-Lagrangian algorithm that approaches the Vlasov equation on a grid of phase space. As this kind of method requires a huge computational(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 is devoted to the numerical simulation of the Vlasov equation using a phase space grid. In contrast to Particle-In-Cell (PIC) methods, which are known to be noisy, we propose a semi-Lagrangian-type method to discretize the Vlasov equation in the two-dimensional phase space. As this kind of method requires a huge computational effort, one has to(More)