Transport of Gyration-Dominated Space Plasmas of Thermal Origin 2: Numerical Solution

A numerical solution has been found for the hyperbolic initial-value problem, which follows from the 16-moment set of equations describing the transport of a plasma in a strong magnetic field. In addition to the time-dependent evolution of mass and momentum, these equations describe the variations in anisotropic temperatures and heat fluxes for both ion and electron species. The numerical solution employs a high-order Godunov method to achieve third-order accuracy in space and second-order accuracy in time. The method includes an approximate Riemann solver which is suitable for a system of equations that cannot entirely be expressed in conservation form. In addition, a new technique has been developed to overcome the stiffness that occurs in regions where plasma flows are strongly reactive. Simple test cases showing correct wave behavior are presented.