Well-Balanced Schemes Based on Elementary Solutions for Kinetic Models of Ionized or Ultra-Relativistic Gas

Well-balanced schemes for two types of (1 + 1)-dimensional kinetic models are set up relying on scattering matrices derived from the explicit so-called elementary solutions of the corresponding stationary equations. A "matrix balancing" (or "matrix equilibration") technique is evoked to ensure the overall mass (and positivity) preservation. The first model is a simplification of edge plasma dynamics close to a wall, like a tokamak divertor, whereas the second one is essentially a rewriting of the Anderson-Witting Bhatnagar-Gross-Krook (BGK) model of relativistic Boltzmann equation for example, photons. Numerical results on coarse grids are provided to illustrate the feasibility of the algorithms.