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

In the recent paper [2], a penalty method is proposed to address the so-called Bohm boundary conditions which are generally imposed to model the limiters, i.e. the walls that intercept in a tokamak the magnetic field lines. This approach is validated by considering a simple one-dimensional hyperbolic system, that constitutes a minimal transport model for ionic density and momentum. In [1] this penalty model is discussed and an improved formulation of the penalty method is proposed. More recently, in [6], a similar model is considered but completed with evolution equations for the ionic and electronic temperatures. Again, a penalty method is proposed to enforce the boundary conditions at the walls.