Vador : Vlasov approximation

This software was developed (or is under development) within the higher education and research community. Its stability can vary (see fields below) and its working state is not guaranteed.
Higher Edu - Research dev card
  • Creation or important update: 17/05/10
  • Minor correction: 17/05/10
  • Index card author: Francis Filbet (ICJ)
  • Theme leader: Violaine Louvet (Institut Camille Jordan)
Keywords
General software features

In general, Particle In Cell (PIC) methods have proven to be a very efficient tool for the numerical simulation of charged particle systems. The main advantage of such methods is that they can adequately give very good results for the low order moments of primary interest in particle beam transport with a fairly small number of particles, and thus make it possible to follow a particle beam for a long time. However, in some cases one may be interested in more detailed collective wave phenomena, which may occur over shorter time scales. Then, the statistical noise inherent in the PIC method can make it difficult to get an accurate description of the phenomenon. A better option for such problems can be to use Vlasov solvers, which discretize the full phase space on a multi-dimensional grid. This procedure is intrinsically devoid of statistical noise and numerical errors are only associated with the discretization of the Vlasov equation on the phase-space grid.

Context in which the software is used

The Vlasov equation describes the evolution of a system of particles under the effects of self-consistent electro magnetic fields. The unknown f(t,x,v) depends on time t, position x, and velocity v. It represents the distribution function of particles (electrons, protons, ions,...) in phase space. This model can be used for the study of beam propagation or of a collisionless plasma.

Publications related to software
  • Convergence of a Finite Volume Scheme for the One Dimensional Vlasov-Poisson System, SIAM J. Numer. Analysis, 39 (2001), no. 4, 1146--1169.
  • Conservative Numerical Schemes for the Vlasov Equation, J. Comput. Physics 172 (2001), no. 1, 166--187, with E. Sonnendrucker and P. Bertrand.
  • Comparison of Eulerian Vlasov Solvers, Comput. Phys. Communications, 150 (2003), no. 3, 247--266, with E. Sonnendrucker.