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In various astrophysics settings it is common to have a two-fluidrelativistic plasma that interacts with the electromagnetic field. While it iscommon to ignore the displacement current in the ideal, classicalmagnetohydrodynamic limit, when the flows become relativistic thisapproximation is less than absolutely well-justified. In such a situation, itis more natural to consider a positively charged fluid made up of positrons orprotons interacting with a negatively charged fluid made up of electrons. Thetwo fluids interact collectively with the full set of Maxwell's equations. As aresult, a solution strategy for that coupled system of equations is sought andfound here. Our strategy extends to higher orders, providing increasingaccuracy. Three important innovations are reported here. In our firstinnovation, the magnetic field within each zone is reconstructed in adivergence-free fashion while the electric field within each zone isreconstructed in a form that is consistent with Gauss' law. In our secondinnovation, a multidimensionally upwinded strategy is presented which ensuresthat the magnetic field can be updated via a discrete interpretation ofFaraday's law and the electric field can be updated via a discreteinterpretation of the generalized Ampere's law. Our third innovation consistsof an efficient design for several popular IMEX schemes so that they providestrong coupling between the finite-volume-based fluid solver and theelectromagnetic fields at high order. Several accuracy analyses are presentedshowing that our method meets its design accuracy in the MHD limit as well asin the limit of electromagnetic wave propagation. Several stringent testproblems are also presented. We also present a relativistic version of the GEMproblem, which shows that our algorithm can successfully adapt to challengingproblems in high energy astrophysics.

journal of computational physics

A High-Order Relativistic Two-Fluid Electrodynamic Scheme with  Consistent Reconstruction of Electromagnetic Fields and a Multidimensional  Riemann Solver for Electromagnetism