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arXiv · 2606.22691

Finite-volume scheme for first-order viscoresistive relativistic magnetohydrodynamics

Ruben Lier·Jay Armas·Oliver Porth
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Abstract

We present a numerical implementation of dissipative relativistic magnetohydrodynamics based on Bemfica-Disconzi-Noronha-Kovtun (BDNK) theory, in which first-order corrections render the equations causal without introducing additional dynamical variables. We show how these corrections can be incorporated in a finite-volume scheme describing the coupled dissipation of energy, momentum, and magnetic field, with the latter treated as a one-form charge. While a minimal set of BDNK terms can convert diffusive equations into telegrapher-type equations, we find that in the ultra-relativistic limit an additional correction is required for the system to behave in a stable and causal manner. With this set of equations, we develop an efficient method for primitive-variable recovery and validate the implementation through an analytical benchmark and various two-dimensional simulations.

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Ruben Lier, Jay Armas, Oliver Porth. 2026-06-21. Finite-volume scheme for first-order viscoresistive relativistic magnetohydrodynamics. https://arxiv.org/abs/2606.22691

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