Relativistic resistive magneto-hydrodynamics code for high-energy heavy-ion collisions

Kouki Nakamura; Takahiro Miyoshi; Chiho Nonaka; Hiroyuki R. Takahashi

doi:10.1140/epjc/s10052-023-11343-y

2023 Impact factor 4.2

Particles and Fields

Open Access

Eur. Phys. J. C (2023) 83: 229
https://doi.org/10.1140/epjc/s10052-023-11343-y

Regular Article - Theoretical Physics

Relativistic resistive magneto-hydrodynamics code for high-energy heavy-ion collisions

Kouki Nakamura¹^,2^a, Takahiro Miyoshi², Chiho Nonaka¹^,2^,3^,4 and Hiroyuki R. Takahashi⁵

¹ Department of Physics, Nagoya University, 464-8602, Nagoya, Japan
² Department of Physics, Hiroshima University, 739-8526, Higashihiroshima, Japan
³ Kobayashi Maskawa Institute, Nagoya University, 464-8602, Nagoya, Japan
⁴ International Institute for Sustainability with Knotted Chiral Meta Matter, Hiroshima University, 739-8511, Higashihiroshima, Japan
⁵ Department of Natural Sciences, Faculty of Arts and Sciences, Komazawa University, 154-8525, Tokyo, Japan

^a knakamura@hken.phys.nagoya-u.ac.jp

Received: 7 November 2022
Accepted: 18 February 2023
Published online: 20 March 2023

Abstract

We construct a relativistic resistive magneto-hydrodynamic (RRMHD) numerical simulation code for high-energy heavy-ion collisions as a first designed code in the Milne coordinates. We split the system of differential equations into two parts, a non-stiff and a stiff part. For the non-stiff part, we evaluate the numerical flux using HLL approximated Riemann solver and execute the time integration by the second-order of Runge–Kutta algorithm. For the stiff part, which appears in Ampere’s law, we integrate the equations using semi-analytic solutions of the electric field. We employ the generalized Lagrange multiplier method to ensure the divergence-free constraint for the magnetic field and Gauss’s law. We confirm that our code reproduces well the results of standard RRMHD tests in the Cartesian coordinates. In the Milne coordinates, the code with high conductivity is validated against relativistic ideal MHD tests. We also verify the semi-analytic solutions of the accelerating longitudinal expansion of relativistic resistive magneto-hydrodynamics in high-energy heavy-ion collisions in comparison with our numerical result. Our numerical code reproduces these solutions.

© The Author(s) 2023

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