Intermediate Modeling between Kinetic Equations and Hydrodynamic Limits: Application to the Spitzer-Harm regime

This work is devoted to the study of a problem resulting from plasma physics: heat transfer of electrons in a plasma close to Maxwellian equilibrium. A formal derivation from the Vlasov equations is proposed. A hierarchy of intermediate models between the kinetic equations and the hydrodynamic limit is described. In particular, a new system
hydrodynamics, integro-differential in nature, is proposed. The system Schurtz and Nicolai appears as a simplification of the system resulting from the diversion. The local existence and uniqueness of the solution of the nonstationary system are established in a simplified framework. The last part is devoted to the implementation of a specific numerical scheme for solving these models. We propose a finite volume approach can be effective on unstructured grids. The accuracy of this scheme to capture specific effects such as kinetic, which may not be reproduced by the asymptotic Spitzer-Harm model.The consistency of this pattern with that of the Spitzer-Harm equation is highlighted, paving the way for a strategy of
coupling between the two models.