A Second-Order Divergence-Constrained Multidimensional Numerical Scheme for Relativistic Two-Fluid Electrodynamics

Abstract

A new multidimensional simulation code for relativistic two-fluid electrodynamics (RTFED) is described. The basic equations consist of the full set of Maxwell's equations coupled with relativistic hydrodynamic equations for separate two charged fluids, representing the dynamics of either an electron-positron or an electron-proton plasma. It can be recognized as an extension of conventional relativistic magnetohydrodynamics (RMHD). Finite resistivity may be introduced as a friction between the two species, which reduces to resistive RMHD in the long wavelength limit without suffering from a singularity at infinite conductivity. A numerical scheme based on HLL (HartenLax-Van Leer) Riemann solver is proposed that exactly preserves the two divergence constraints for Maxwell's equations simultaneously. Several benchmark problems demonstrate that it is capable of describing RMHD shocks/discontinuities at long wavelength limit, as well as dispersive characteristics due to the two-fluid effect appearing at small scales. This shows that the RTFED model is a promising tool for high energy astrophysics application.

A high-order relativistic two-fluid electrodynamic scheme with consistent reconstruction of electromagnetic fields and a multidimensional Riemann solver for electromagnetism

“…In the above two equations η is a parameter that parametrizes the resistivity. With the above definitions, it has been shown by Amano [3] that one can retrieve the resistive MHD limit of Komissarov [52].…”

Resistive and Multi-fluid RMHD on Graphics Processing Units

“…To satisfy these constraints we use the method of hyperbolic divergence cleaning for each model (Komissarov 2007). It is worth pointing out that Amano (2016) uses the constrained transport method for the two-fluid RMHD model, making the argument that divergence cleaning may not be suitable. We have found that, for the applications in which we use METHOD, divergence cleaning works well, and that implementing this method requires very little change to any existing code.…”

“…There are a number methods for this, see e.g. Amano (2016); Dionysopoulou et al (2013) and Palenzuela et al (2009), of which we have implemented the latter two. In contrast to ideal RMHD, which requires a two-dimensional root-find to determine the primitive variables (Antón et al 2010), resistive RMHD only requires a single residual to be minimised.…”

“…For the two-fluid RMHD model we use the initial data from Amano (2016), given by Equations (14). At high enough resolutions, we can see the onset of the two-fluid effect as expected.…”

Multidimensional Hall magnetohydrodynamics with isotropic or anisotropic thermal pressure: Numerical scheme and its validation using solitary waves

“…The electron pressure gradients are neglected in the presented approach, which formally corresponds to cold electrons limit. Possible extensions of the equations in the context of numerical simulations, like e.g., two-fluid [30] (including relativistic effects [31,32]) or multi-fluid [33] models have been considered in the literature.…”