The Euler-Lorentz model consists of the Euler equations for a charged particle gas subject to the Lorentz force. It describes the evolution of a plasma submitted to an electro-magnetic field. Our goal is to build a numerical approximation of the solution of such a model when the applied magnetic field is supposed to be strong. Under this hypothesis, the gyroperiod of the considered particles becomes very small, so we have to deal with a small parameter. The aim of this project is to build a finite volume scheme which can simulate such a model for any values of this small parameter, and which is consistent with the limit model when the small parameter tends to zero. Such a scheme is called an Asymptotic-Preserving scheme. Recently, the 2D isothermal monofluid case has been studied in a series of works [1, 2] and current works [3, 4] extends this model to the mono-fluid full Euler equations. The aim of the project is to extend this work to the bi-fluid (electrons and ions) case with a coupling through an electric field computed via the quasineutrality constraint.
[1] P. Degond, F. Deluzet, A. Sangam, M.-H. Vignal, An asymptotic-Preserving Scheme for the Euler equations in a strong magnetic field, J. Comput. Phys. 228 (2009), pp. 3540-3558.
[2] P. Degond, F. Deluzet, A. Mouton, A numerical investigation of the full Euler-Lorentz model with large magnetic field (in preparation).
[3] S. Brull, P. Degond, F. Deluzet, Numerical degenerate elliptic problems and their applications to magnetized plasma simulation (submitted).
[4] S. Brull, F. Deluzet, A. Mouton, Numerical resolution of an anisotropic non-linear diffusion problem (in preparation).
Project leaders : P. Degond and F. Deluzet.
Other collaborators : S. Brull.