March  2009, 2(1): 39-80. doi: 10.3934/krm.2009.2.39

The multi-water-bag equations for collisionless kinetic modeling

1. 

Laboratoire de Physique des Milieux Ionisés et Applications, UMR Nancy-Université CNRS 7040, France

2. 

Laboratoire J.A. Dieudonné, UMR CNRS 6621, Université de Nice Sophia-Antipolis, Parc Valrose, 06108 Nice Cedex 02, France, France

3. 

Laboratoire de Physique des Milieux Ionisés et Applications, UMR Nancy-Université CNRS 7040, Université Henri Poincaré, Bd des Aiguillettes, B.P. 239, 54506 Vandoeuvre-lès-Nancy Cedex, France

Received  November 2008 Revised  December 2008 Published  January 2009

In this paper we consider the multi-water-bag model for collisionless kinetic equations. The multi-water-bag representation of the statistical distribution function of particles can be viewed as a special class of exact weak solution of the Vlasov equation, allowing to reduce this latter into a set of hydrodynamic equations while keeping its kinetic character. After recalling the link of the multi-water-bag model with kinetic formulation of conservation laws, we derive different multi-water-bag (MWB) models, namely the Poisson-MWB, the quasineutral-MWB and the electromagnetic-MWB models. These models are very promising because they reveal to be very useful for the theory and numerical simulations of laser-plasma and gyrokinetic physics. In this paper we prove some existence and uniqueness results for classical solutions of these different models. We next propose numerical schemes based on Discontinuous Garlerkin methods to solve these equations. We then present some numerical simulations of non linear problems arising in plasma physics for which we know some analytical results.
Citation: Nicolas Besse, Florent Berthelin, Yann Brenier, Pierre Bertrand. The multi-water-bag equations for collisionless kinetic modeling. Kinetic & Related Models, 2009, 2 (1) : 39-80. doi: 10.3934/krm.2009.2.39
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