A highorder relativistic twofluid electrodynamic scheme with consistent reconstruction of electromagnetic fields and a multidimensional Riemann solver for electromagnetism
Abstract
In various astrophysics settings it is common to have a twofluid relativistic plasma that interacts with the electromagnetic field. While it is common to ignore the displacement current in the ideal, classical magnetohydrodynamic limit, when the flows become relativistic this approximation is less than absolutely welljustified. In such a situation, it is more natural to consider a positively charged fluid made up of positrons or protons interacting with a negatively charged fluid made up of electrons. The two fluids interact collectively with the full set of Maxwell's equations. As a result, a solution strategy for that coupled system of equations is sought and found here. Our strategy extends to higher orders, providing increasing accuracy. The primary variables in the Maxwell solver are taken to be the faciallycollocated components of the electric and magnetic fields. Consistent with such a collocation, three important innovations are reported here. The first two pertain to the Maxwell solver. In our first innovation, the magnetic field within each zone is reconstructed in a divergencefree fashion while the electric field within each zone is reconstructed in a form that is consistent with Gauss' law. In our second innovation, a multidimensionally upwinded strategy is presented which ensures thatmore »
 Authors:
 Physics Department, University of Notre Dame (United States)
 Department of Earth and Planetary Science, University of Tokyo, Tokyo 1130033 (Japan)
 Publication Date:
 OSTI Identifier:
 22572338
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Journal of Computational Physics; Journal Volume: 318; Other Information: Copyright (c) 2016 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGORITHMS; ASTROPHYSICS; CONSERVATION LAWS; CURRENT DENSITY; ELECTRIC FIELDS; ELECTRODYNAMICS; ELECTROMAGNETIC FIELDS; ELECTROMAGNETIC RADIATION; ELECTROMAGNETISM; EQUATIONS; FLUIDS; MAGNETIC FIELDS; MAGNETOHYDRODYNAMICS; RELATIVISTIC PLASMA; RELATIVISTIC RANGE; STOKES LAW; WAVE PROPAGATION
Citation Formats
Balsara, Dinshaw S., Email: dbalsara@nd.edu, Amano, Takanobu, Email: amano@eps.s.utokyo.ac.jp, Garain, Sudip, Email: sgarain@nd.edu, and Kim, Jinho, Email: jkim46@nd.edu. A highorder relativistic twofluid electrodynamic scheme with consistent reconstruction of electromagnetic fields and a multidimensional Riemann solver for electromagnetism. United States: N. p., 2016.
Web. doi:10.1016/J.JCP.2016.05.006.
Balsara, Dinshaw S., Email: dbalsara@nd.edu, Amano, Takanobu, Email: amano@eps.s.utokyo.ac.jp, Garain, Sudip, Email: sgarain@nd.edu, & Kim, Jinho, Email: jkim46@nd.edu. A highorder relativistic twofluid electrodynamic scheme with consistent reconstruction of electromagnetic fields and a multidimensional Riemann solver for electromagnetism. United States. doi:10.1016/J.JCP.2016.05.006.
Balsara, Dinshaw S., Email: dbalsara@nd.edu, Amano, Takanobu, Email: amano@eps.s.utokyo.ac.jp, Garain, Sudip, Email: sgarain@nd.edu, and Kim, Jinho, Email: jkim46@nd.edu. 2016.
"A highorder relativistic twofluid electrodynamic scheme with consistent reconstruction of electromagnetic fields and a multidimensional Riemann solver for electromagnetism". United States.
doi:10.1016/J.JCP.2016.05.006.
@article{osti_22572338,
title = {A highorder relativistic twofluid electrodynamic scheme with consistent reconstruction of electromagnetic fields and a multidimensional Riemann solver for electromagnetism},
author = {Balsara, Dinshaw S., Email: dbalsara@nd.edu and Amano, Takanobu, Email: amano@eps.s.utokyo.ac.jp and Garain, Sudip, Email: sgarain@nd.edu and Kim, Jinho, Email: jkim46@nd.edu},
abstractNote = {In various astrophysics settings it is common to have a twofluid relativistic plasma that interacts with the electromagnetic field. While it is common to ignore the displacement current in the ideal, classical magnetohydrodynamic limit, when the flows become relativistic this approximation is less than absolutely welljustified. In such a situation, it is more natural to consider a positively charged fluid made up of positrons or protons interacting with a negatively charged fluid made up of electrons. The two fluids interact collectively with the full set of Maxwell's equations. As a result, a solution strategy for that coupled system of equations is sought and found here. Our strategy extends to higher orders, providing increasing accuracy. The primary variables in the Maxwell solver are taken to be the faciallycollocated components of the electric and magnetic fields. Consistent with such a collocation, three important innovations are reported here. The first two pertain to the Maxwell solver. In our first innovation, the magnetic field within each zone is reconstructed in a divergencefree fashion while the electric field within each zone is reconstructed in a form that is consistent with Gauss' law. In our second innovation, a multidimensionally upwinded strategy is presented which ensures that the magnetic field can be updated via a discrete interpretation of Faraday's law and the electric field can be updated via a discrete interpretation of the generalized Ampere's law. This multidimensional upwinding is achieved via a multidimensional Riemann solver. The multidimensional Riemann solver automatically provides edgecentered electric field components for the Stokes lawbased update of the magnetic field. It also provides edgecentered magnetic field components for the Stokes lawbased update of the electric field. The update strategy ensures that the electric field is always consistent with Gauss' law and the magnetic field is always divergencefree. This collocation also ensures that electromagnetic radiation that is propagating in a vacuum has both electric and magnetic fields that are exactly divergencefree. Coupled relativistic fluid dynamic equations are solved for the positively and negatively charged fluids. The fluids' numerical fluxes also provide a selfconsistent current density for the update of the electric field. Our reconstruction strategy ensures that fluid velocities always remain subluminal. Our third innovation consists of an efficient design for several popular IMEX schemes so that they provide strong coupling between the finitevolumebased fluid solver and the electromagnetic fields at high order. This innovation makes it possible to efficiently utilize high order IMEX time update methods for stiff source terms in the update of high order finitevolume methods for hyperbolic conservation laws. We also show that this very general innovation should extend seamlessly to Runge–Kutta discontinuous Galerkin methods. The IMEX schemes enable us to use large CFL numbers even in the presence of stiff source terms. Several accuracy analyses are presented showing that our method meets its design accuracy in the MHD limit as well as in the limit of electromagnetic wave propagation. Several stringent test problems are also presented. We also present a relativistic version of the GEM problem, which shows that our algorithm can successfully adapt to challenging problems in high energy astrophysics.},
doi = {10.1016/J.JCP.2016.05.006},
journal = {Journal of Computational Physics},
number = ,
volume = 318,
place = {United States},
year = 2016,
month = 8
}

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