Moments conservation in adaptive Vlasov solver

We previously developed an adaptive semi-Lagrangian solver using a multiresolution analysis based on interpolets which are a kind of interpolating wavelets introduced by Deslauriers and Dubuc. This paper introduces a new multiresolution approximation for this solver which allows to conserve moments up to any order by using the lifting method introduced by Sweldens

Adaptive 2-D Vlasov Simulation of Particle Beams

International audienceThis paper presents our progress for the solution of the 4D Vlasov equation on a grid of the phase space, using two adaptive methods. We briefly recall the principle of the two methods and then particularly focus on computer science features - as data structures or parallelization - for the efficient implementation of the methods. Some relevant numerical results are presented

Galerkin discontinuous approximation of the MHD equations

International audienceIn this report, we address several aspects of the approximation of the MHD equations by a Galerkin Discontinuous finite volume schemes. This work has been initiated during a CEMRACS project in july and august 2008 in Luminy. The project was entitled GADMHD (for GAlerkin Discontinuous approximation for the Magneto-Hydro-Dynamics). It has been supported by the INRIA CALVI project

Adaptive two-dimensional Vlasov simulation of heavy ion beams

International audienceWe present very first results for the solution of the paraxial Vlasov equation on the full 4D transverse phase-space with a new adaptive code

Numerical methods for hyperbolic and kinetic problems. CEMRACS 2003, summer research center in mathematics and advances in scientific computing, July 21 -- August 29, 2003, CIRM, Marseille, France.

Hyperbolic and kinetic equations arise in a large variety of industrial problems. For this reason, the CEMRACS summer research center held at CIRM in Luminy in 2003 was devoted to this topic. During a six-week period, junior and senior researchers worked full time on several projects proposed by industry and academia. Most of this work was completed later on, and the results are now reported in the present book. The articles address modelling issues as well as the development and comparisons of numerical methods in different situations. The applications include multi-phase flow, plama physics, quantum particle dynamics, radiative transfer, sprays and aeroacoustics. The text is aimed at researchers and engineers interested in modelling and numerical simulation of hyperbolic and kinetic problems arising from applications

Comparison of two Eulerian solvers for the four-dimensional Vlasov equation: Part II

International audienceIn this second part, we carry out a numerical comparison between twoVlasovsolvers, which solve directly the Vlasovequation on a grid of the phase space. The two methods are based on the semi-Lagrangian method as presented in Part I: the first one (LOSS, local splines simulator) uses a uniform mesh of the phase space whereas the second one (OBI, ondelets based interpolation) is an adaptive method. The numerical comparisons are performed by solving the four-dimensionalVlasovequation for some classical problems of plasma and beam physics. We shall also investigate the speedup and the CPU time as well as the compression rate of the adaptive method which are important features because of the size of the problems

Comparison of two Eulerian solvers for the four-dimensional Vlasov equation: Part I

International audienceThis paper presents two methods for solving the four-dimensional Vlasov equation on a grid of the phase space. The two methods are based on the semi-Lagrangian method which consists in computing the distribution function at each grid point by following the characteristic curve ending there. The first method reconstructs the distribution function using local splines which are well suited for a parallel implementation. The second method is adaptive using wavelets interpolation: only a subset of the grid points are conserved to manage data locality. Numerical results are presented in the second part

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

A local time-stepping Discontinuous Galerkin algorithm for the MHD system

International audienceThis work is devoted to the simulation of the Magneto-Hydro-Dynamics (MHD) equations on unstructured meshes. The starting point is the Discontinuous Galerkin (DG) method, semi-discrete in space. For the time integration, we choose the Adams-Bashforth scheme. This scheme allows very easily local time-stepping on the smallest cells of the mesh. Finally, we present several numerical experiments.Ce travail est consacré à la simulation des équations de la Magnéto-Hydro-Dynamique (MHD) sur des maillages complètement déstructurés. Le point de départ est la méthode de Galerkin Discontinue (DG) semi-discrétisée en espace. Pour l'approximation en temps, nous utilisons le schéma multi-pas d'Adams-Bashforth. Ce schéma permet l'utilisation de pas de temps locaux sur les petites mailles, ce qui conduit pour certains maillages à des gains considérables de temps de calcul. Enfin, nous présentons diverses expériences numériques