Asymptotic-Preserving Schemes for Fluid Models of Plasmas

Pierre Degond (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219

These notes summarize a series of works related to the numerical approximation of plasma fluid problems. We construct so-called 'Asymptotic-Preserving' schemes which are valid for a large range of values (from very small to order unity) of the dimensionless parameters that appear in plasma fluid models. Specifically, we are interested in two parameters, the scaled Debye length which quantifies how close to quasi-neutrality the plasma is, and the scaled cyclotron period, which is inversely proportional to the magnetic field strength. We will largely focus on the ideas, in order to enable the reader to apply these concepts to other situations.

Domaines: Physique mathématique [math-ph]

Pierre Degond. Asymptotic-Preserving Schemes for Fluid Models of Plasmas. N. Crouseilles, H. Guillard, B. Nkonga, E. Sonnendrücker. Numerical models for fusion, collection Panoramas et synthèses, édité par la SMF, 39-40, Société mathématique de France, pp.1-90, 2013, Panoramas et synthèses, 978-28529-776-6. ⟨hal-00584718⟩