Multi-component multi-scale hydrodynamic plasma flow models in mechanical and thermal disequilibria

Abstract

The present work is motivated by the mixing mechanism in inertial confinement fusion (ICF), which remarkably degrades the ignition performance. The mixing is a direct result of velocity disequilibrium and affected by temperature disequilibrium.To deal with these disequilibria, we propose a fully-disequilibrium hydrodynamic model (termed as Baer-Nunziato-Zeldovich model or BNZ model) with 9 equations, 4 temperatures (two for ions, and two for electrons), 4 pressures (two for ions, and two for electrons) and 2 ion velocities for two-component dense plasma flows. The model can be used for describing both grain and atomic mixing by choosing corresponding relaxation mechanism. The derivation starts from a multi-component conservative entropy-dissipative Bhatnagar-Gross-Krook (BGK) model to obtain a 14-equation model. It is then reduced to more practical 9-equation BNZ model and further to simpler 8-equation model, 6-equation model (the Kapila-Zeldovich model or the KZ model), and the 5-equation model. The reductions are performed on the basis of various relaxation time evaluations, the plasma neutrality and the smallness of the electron mass. The models are thermodynamics-compatible, and capable of dealing with mechanical and thermal disequilibria at both atomic and grain scales. Moreover, the corresponding hydrodynamic subsystems are shown to be hyperbolic and solved with the Godunov finite volume method. The BNZ model and solution methods are verified and validated by some benchmark problems and 1D-2D comparisons. We then consider the velocity, pressure and temperature disequilibria during the passage of an ablation shock in ICF.