Finite-volume scheme for first-order viscoresistive relativistic magnetohydrodynamics

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.