SimultaneousApproximationTerm based Boundary Discretization for Moment Equations of Rarefied Gas Dynamics Abstract   Previous works have developed boundary conditions that lead to the      L    2     boundedness of solutions to the linearised moment equations. Here we present a spatial discretization that preserves the      L    2     stability by recovering integrationbyparts over the discretized domain and by imposing boundary conditions using a simultaneousapproximationterm (SAT). We develop three different forms of the SAT using: (i) characteristic splitting of moment equationu0027s boundary conditions; (ii) decoupling of moments in moment equations; and (iii) characteristic splitting of Boltzmann equationu0027s boundary conditions. We discuss how the first two forms differ in terms of their usage and implementation. We show that the third form is equivalent to using an upwind kinetic numerical flux along the boundary, and we argue that even though it provides stability, it prescribes the incorrect number of boundary conditions. Using benchmark problems, we compare the accuracy of moment solutions computed using different SATs. Our numerical experiments also provide new insights into the convergence of moment approximations to the Boltzmann equationu0027s solution.

Numerical Resolution of a Three Temperature Plasma Model This paper is devoted to the numerical approximation of a three temperature plasma model: one for the ions, one for the electrons and one for the radiation (photons). A reformulation of the model is proposed that allows to build a convex combinationbased scheme that unconditionally satisfies a maximum principle, at each subiteration of the nonlinear iterative process. This yields a very robust scheme that can handle stiff source terms. In addition, the methodology is extended to include the contribution of a radiative flux (Rosseland diffusion approximation) and electronic and ionic conductivities (Spitzerxe2x80x93Harm diffusion approximation). Several numerical results are carried out to demonstrate the interest of the numerical approach.