High order approximation of a tokamak edge plasma transport minimal model with Bohm boundary conditions

To address the so-called Bohm boundary conditions, generally imposed at the walls that intercept in a tokamak the magnetic field lines, we consider a simple one-dimensional hyperbolic system that constitutes a minimal transport model for ionic density and momentum. We show that as soon as the solution is smooth, a spectrally accurate approximation can be obtained. To this end, we describe a stabilized spectral element method (SEM) and propose a direct imposition of the Bohm boundary condition in an explicit time marching.