Comparison of Eulerian Vlasov Solvers

Abstract : Vlasov methods which instead of following the particle trajectories solve the Vlasov equation on a grid of phase space have proven to be an efficient alternative to the Particle In Cell method for some specific problems, in particular those where a good precision is needed for the distribution function in regions of phase space where it is small. Gridded Vlasov methods have the advantage of being completely free of numerical noise, however the discrete formulations contain some other numerical artifacts, like damping, which are necessary for such methods to be stable and deal with filamentation which is inherent to the Vlasov-Poisson equations. We shall compare in this paper different types of methods solving the Vlasov equation on a grid in phase space: the semi-Lagrangian method, the finite volume method, the spectral method, and a method based on a finite difference scheme conserving exactly several invariants of the system. Moreover for each of those classes of methods, we shall compare different interpolation or reconstruction procedures in this respect, always keeping in mind the cost in memory as well as in CPU time is a very important issue because of the size of the problem which is defined on a grid in phase space which can be up to six-dimensional.
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Pré-publication, Document de travail
2001
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  • HAL Id : hal-00129663, version 1

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Francis Filbet, Eric Sonnendrücker. Comparison of Eulerian Vlasov Solvers. 2001. 〈hal-00129663〉

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