A Two-fluid Model for Plasma with Prandtl Number Correction

Abstract

A two-fluid model is derived from the plasma kinetic equations using the moment model reduction method. The moment method we adopt was recently developed with a globally hyperbolic regularization where the moment model attained is locally well-posed in time. Based on the hyperbolic moment model with well-posedness, the Maxwellian iteration method is utilized to get the closure relations for the resulted two-fluid model. By taking the Shakhov collision operator in the Maxwellian iteration, the two-fluid model inherits the correct Prandtl number from the plasma kinetic equations. The new model is formally the same as the five-moment two-fluid model except for the closure relations, where the pressure tensor is anisotropic and the heat flux is presented. This provides the model the capacity to depict problems with anisotropic pressure tensor and large heat flux.