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

We construct a relativistic resistive magneto-hydrodynamic (RRMHD) numerical simulation code for high-energy heavy-ion collisions. 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 a comparison with our numerical result. Our numerical code reproduces these solutions.