Results 1 -
8 of
8
How to predict accurate wavelet grids in adaptive semi-Lagrangian schemes
- in "ESAIM Proceedings", 2009, to appear. Activity Report INRIA 2009
"... Résumé. Je présente dans cet article un nouveau schéma semi-Lagrangien a ̀ base d’ondelettes pour l’approximation de problèmes de transport associés a ̀ des flots réguliers. Cette méthode s’inspire de celle proposée par Besse, Filbet, Gutnic, Paun et Sonnendrücker [1], mais s’en distingue ..."
Abstract
-
Cited by 2 (0 self)
- Add to MetaCart
(Show Context)
Résumé. Je présente dans cet article un nouveau schéma semi-Lagrangien a ̀ base d’ondelettes pour l’approximation de problèmes de transport associés a ̀ des flots réguliers. Cette méthode s’inspire de celle proposée par Besse, Filbet, Gutnic, Paun et Sonnendrücker [1], mais s’en distingue notamment par le fait qu’elle s’articule autour de la notion de bonne adaptation d’un arbre d’ondelettes a ̀ une fonction donnée. De plus, elle s’accompagne d’une estimation d’erreur a priori. Dans un travail précédent effectue ́ en collaboration avec Mehrenberger [3], nous avions conçu un premier schéma adaptatif semi-Lagrangien base ́ sur des maillages multi-échelles et hiérarchiques. Notre méthode consistait a ̀ prédire un nouveau maillage a ̀ chaque pas de temps par une stratégie peu coûteuse, puis a ̀ le réadapter suivant la régularite ́ de la solution numérique transportée. Par une anal-yse rigoureuse, nous avions établi qu’une simple application de notre algorithme de prédiction et de correction suffisait a ̀ garantir une estimation d’erreur a priori. Le schéma présente ́ ici met en œuvre des idées semblables, mais dans un cadre différent. La propriété d’être (fortement) bien adaptate ́ a ̀ une fonction donnée est donc redéfinie pour des arbres d’ondelettes, et l’on peut montrer qu’elle est (faiblement) préservée par une stratégie de prédiction, toujours peu coûteuse, qui transporte les grilles d’ondelettes le long de flots réguliers. En conséquence, il est possible
High order and energy preserving discontinuous Galerkin methods for the Vlasov-Poisson system
, 2012
"... Abstract. We present a computational study for a family of discontinuous Galerkin meth-ods for the one dimensional Vlasov-Poisson system, recently introduced in [4]. We introduce a slight modification of the methods to allow for feasible computations while preserving the properties of the original m ..."
Abstract
-
Cited by 2 (0 self)
- Add to MetaCart
(Show Context)
Abstract. We present a computational study for a family of discontinuous Galerkin meth-ods for the one dimensional Vlasov-Poisson system, recently introduced in [4]. We introduce a slight modification of the methods to allow for feasible computations while preserving the properties of the original methods. We study numerically the verification of the theoretical and convergence analysis, discussing also the conservation properties of the schemes. The methods are validated through their application to some of the benchmarks in the simulation of plasma physics. Numerical simulation has become a major tool for understanding the complex behavior of a plasma or a particle beam in many situations. This is due not only to the large number of physical applications and technological implications of the behavior of plasmas, but also to the intrinsic difficulties of the models used to describe such behavior. In fact, it was recog-nized long time ago that there does not exist any fully satisfactory macroscopic model (fluid equations) which can be used to describe the particle interaction in laser-fusion problems. In contrast, microscopic models (kinetic equations) can provide a more accurate description of the plasmas.
THEME
"... 3.1. Kinetic models for plasma and beam physics 2 3.1.1. Models for plasma and beam physics 3 ..."
Abstract
- Add to MetaCart
3.1. Kinetic models for plasma and beam physics 2 3.1.1. Models for plasma and beam physics 3
Project-Team Calvi Scientific Computing and Visualization
"... c t i v it y e p o r t ..."
(Show Context)
The semi-Lagrangian method on curvilinear grids
, 2015
"... We study the semi-Lagrangian method on curvilinear grids. The clas-sical backward semi-Lagrangian method [1] preserves constant states but is not mass conservative. Natural reconstruction of the field permits nev-ertheless to have at least first order in time conservation of mass, even if the spatia ..."
Abstract
- Add to MetaCart
(Show Context)
We study the semi-Lagrangian method on curvilinear grids. The clas-sical backward semi-Lagrangian method [1] preserves constant states but is not mass conservative. Natural reconstruction of the field permits nev-ertheless to have at least first order in time conservation of mass, even if the spatial error is large. Interpolation is performed with classical cubic splines and also cubic Hermite interpolation with arbitrary reconstruction order of the derivatives. High odd order reconstruction of the derivatives is shown to be a good ersatz of cubic splines which do not behave very well as time step tends to zero. A conservative semi-Lagrangian scheme along the lines of [2] is then described; here conservation of mass is au-tomatically satisfied and constant states are shown to be preserved up to first order in time.1 1
Error Estimates of Runge-Kutta Discontinuous Galerkin Methods for the Vlasov-Maxwell System
, 2014
"... ar ..."
(Show Context)
