Development of a Discontinuous Galerkin fluid solver for argon plasma-sheath*

The understanding of plasma-sheath formation phenomenon is of vital importance for a great variety of engineering fields, that range from electric propulsion for space applications  to magnetically confined fusion devices, from development of thermal protection systems for hypersonic flows till the study of development of arcing in microelectronics. 

The aim of this work is to develop a fluid solver that will combine a reasonable computational cost with the high order spatial accuracy that the Discontinuous Galerkin discretization is able to achieve: in order to describe a mixture of argon plasma (electrons, single-charged ions, neutral atom) we are going to compare two different approaches, the multifluid and the multicomponent modeling, in order to assess their performance under different pressure conditions; the governing equations used in both cases remind of the Navier-Stokes equations (as they account for conservation of density, momentum and, eventually, energy) coupled to the Poisson equation, ensuring charge conservation throughout the entire domain. The intrinsic multiscale character of the problem (which is in large part due to the large disparity in mass between electrons and ions/neutrals, that reflects naturally in strong thermal nonequilibrium, i.e. the electron temperature is higher than the heavy temperature) is described and overcome by taylor-made ESDIRK time integration.

Results obtained are critically compared to well-known solution from literature providing the basis for future development towards more complex mixtures: the chosen high order framework allows to adequately resolve sharp gradients in the solution, typical of the plasma-sheath transition, and the implemented implicit time-discretization is able to overcome the strict  stability constraints for this models.