Hyperbolic Algorithm for Coupled Plasma/Electromagnetic Fields Including Conduction and Displacement Currents

摘要

A numerical procedure that applies to both the magnetic diffusion and wave propagation regimes of a general plasma/electromagnetic system is presented. The method solves the full Maxwell equations, with or without displacement current, in combination with the Navier-Stokes equations. The combined system is placed in a fully coupled conservation form and embedded in a dual-time formulation that enables classical hyperbolic solution algorithms to be effective across the wave and diffusion limits of the Maxwell equations. The dual-time formulation introduces a pseudotime with an artificial speed of light that includes divergence constraints that are driven to zero by means of a Lagrange multiplier technique. The validity of the algorithm is first established by verifying results obtained with the hyperbolic procedure for the diffusion form of the telegraph equation against analytical solutions. Additional verification for the electromagnetic equations is obtained by comparison with magnetic diffusion simulations obtained from the MACH2 code. Representative numerical calculations are presented for both the wave and magnetic diffusion limits to illustrate the importance of a solution technique that handles all regimes, from insulators to conductors.