Vlasov simulations on an adaptive phase-space grid

The numerical resolution of the Vlasov equation is usually performedby particle methods (PIC) which consist in approximating the plasma bya finite number of particles. This method allows to obtain satisfying results with a relatively smallnumber of particles. However, it is well known that, in some cases,the numerical noise inherent to the particle method becomes tooimportant to have an accurate description of the distribution functionin phase space. To remedy to thisproblem, methods discretizing the Vlasov equation on a mesh of phasespace have been proposed. The major drawback of Vlasov methods using a uniform and fixed mesh is thattheir numerical cost is high, which makes them rather inefficient whenthe dimension of phase-space grows. For this reason we areinvestigating a method using an adaptive mesh. The adaptivemethod is overlayed to a classical semi-Lagrangian method which isbased on the conservation of the distribution function alongparticle trajectories. The phase-space grid is updated using amultiresolution technique based on interpolating wavelets

Convergence of Finite Volume Approximations for a Nonlinear Elliptic-Parabolic Problem: a ``Continuous'' Approach.

International audience"We study the approximation by finite volume methods of the modelparabolic-elliptic problem $b(v)_t=div (|Dv|^{p-2} Dv)$ on$(0,T)imesOmegasubset RimesR^d$ with an initial conditionand the homogeneous Dirichlet boundary condition. Because of thenonlinearity in the elliptic term, a careful choice of the gradient approximation is needed.We prove the convergence of discrete solutions to a solution ofthe continuous problem as the discretization step $h$ tends to $0$,under the main hypotheses that the approximation of the operator$div(|Dv|^{p-2} Dv)$ provided by the finite volume scheme is still monotone and coercive, and that the gradient approximationis exact on the affine functions of $xinOmega$. An example of such a scheme is given for a class of two-dimensional meshes dual to triangular meshes, in particular for structured rectangular andhexagonal meshes.The proof uses the rewriting of the discrete problem under a``continuous'' form. This permits us to directly apply theAlt-Luckhaus variational techniques known in the continuous case.

New early Mesozoic Brachiopods from southern Turkey

New Late Triassic and Early Jurassic brachiopod faunas are described from the Taurus Mountains in Southern Turkey. They include the distinctive Norian rhynchonellid Halorella amphitoma (not previously recorded from Turkey), the aberrant Upper Norian rhynchonellid Carapezzia (only previously recorded from Austria and Sicily) and Sinemurian or Pliensbachian faunas. The significance of these typically North European faunas in a Tethyan realm is discusse

First order Two-Scale Particle-in-Cell numerical method for the Vlasov equation

The aim of this work is to build an accurate numerical method for the simulation of the long time evolution of the Vlasov solution fε with an electric field Eε = E0 + εE1 for small ε. To this purpose, we use the Two-Scale Convergence to determine a first order approximation F + εF1 of fε. Then, by means of particle approximations we build an algorithm which is intended for providing a numerical approximation of F + εF1. <br> On cherche à construire une méthode numérique pour l’évolution en temps long de la solution fε de l’équation de Vlasov avec un champ électrique Eε = E0 + εE1 pour ε petit. À cet effet, on utilise la théorie de la convergence à deux échelles pour obtenir une approximation d’ordre un F + εF1 de fε, puis une méthode particulaire pour construire l’algorithme d’approximation numérique de F + εF1