BibSonomy 
CiteUlike 
Del.icio.us 
Digg 
Facebook 
Mendeley
TwitterHybrid model for the Coupling of an Asymptotic Preserving scheme with the Asymptotic Limit model: The One Dimensional Case⋆
Pierre Degond1,2, Fabrice Deluzet1,2, Dario Maldarella3, Jacek Narski1,2, Claudia Negulescu4 and Martin Parisot5
1 Université de Toulouse, UPS, INSA, UT1, UTM, Institut de Mathématiques de Toulouse, F-31062 ; Toulouse, France
2 CNRS, Institut de Mathématiques de Toulouse UMR 5219, F-31062 Toulouse, France
3 Department of Mathematics and CMCS; University of Ferrara, Via Macchiavelli ; 35 I-44100 Ferrara, Italy
4 CMI/LATP (UMR 6632), Université de Provence ; 39, rue Joliot Curie ; 13453 Marseille Cedes, France
5 Project-Team SIMPAF–INRIA Lille-Nord Europe ; Park Plazza, 40 avenue Halley ; F-59650 Villeneuve d’Ascq cedex, France
In this paper a strategy is investigated for the spatial coupling of an asymptotic preserving scheme with the asymptotic limit model, associated to a singularly perturbed, highly anisotropic, elliptic problem. This coupling strategy appears to be very advantageous as compared with the numerical discretization of the initial singular perturbation model or the purely asymptotic preserving scheme introduced in previous works [3, 5]. The model problem addressed in this paper is well suited for the simulation of a plasma in the presence of a magnetic field, whose intensity may vary considerably within the simulation domain.
This work has been supported by the Marie Curie Actions of the European Commission under the contract DEASE (MEST-CT-2005-021122), by the French ’Commissariat à l’Energie Atomique (CEA)’ under contracts ELMAG (CEA-Cesta 4600156289), and GYRO-AP (Euratom-CEA V 3629.001), by the Agence Nationale de la Recherche (ANR) under contract IODISEE (ANR-09-COSI-007-02), by the Fondation Sciences et Technologies pour l’Aéronautique et l’Espace (STAE) under contract PLASMAX (RTRA-STAE/2007/PF/002) and by the Scientific Council of the Université Paul Sabatier, under contract MOSITER. Support from the French magnetic fusion programme fédération de recherche sur la fusion par confinement magnétique is also acknowledged. The first two authors would like to express their gratitude to G. Gallice and C. Tessieras from CEA-Cesta for bringing their attention to this problem, to G. Falchetto, X. Garbet and M. Ottaviani from CEA-Cadarache, for their constant support to this research program.
© EDP Sciences, SAIM 2011