Thermodynamic analysis and numerical resolution of a turbulent - fully ionized plasma flow model.

This paper is devoted to the modeling and numerical resolution of a non-dissipative compressible turbulent plasma flow model involving three temperatures (turbulence, ions and electrons). The first step is to derive such a model. To do this, an analysis of the Reynolds averaged Euler equations (the k-model) is carried out. It is shown that thermodynamic requirements enable the derivation of an equation of state for turbulent variables. This equation of state is of the same type as those of an ideal gas. In this context, the various thermodynamic variables of turbulence can be obtained (energy, pressure, temperature etc.). This hyperbolic conservative model has exactly the same structure as the two temperatures plasma model of Zel?dovich. Thanks to the clear structure of these two models, the turbulent plasma model is derived and involves three temperatures. The second step is to derive an accurate numerical scheme for its solution. A linearized Riemann solver and a positive HLLC type solver are derived and embedded into a conventional Godunov scheme. It is shown that this method requires important corrections to preserve contact discontinuities and temperatures monotonicity. The corrections are based upon a non-conservative formulation of the turbulence and electrons energy equations, while total energy conservation is preserved. The modified method behaves correctly with contacts and shocks. [ABSTRACT FROM AUTHOR]