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We describe a novel Godunov-type numerical method for solving the equationsof resistive relativistic magnetohydrodynamics. In the proposed approach, thespatial components of both magnetic and electric fields are located at zoneinterfaces and are evolved using the constrained transport formalism. Directapplication of Stokes' theorem to Faraday's and Ampere's laws ensures that theresulting discretization is divergence-free for the magnetic field andcharge-conserving for the electric field. Hydrodynamic variables retain,instead, the usual zone-centred representation commonly adopted infinite-volume schemes. Temporal discretization is based on Runge-Kuttaimplicit-explicit (IMEX) schemes in order to resolve the temporal scaledisparity introduced by the stiff source term in Ampere's law. The implicitstep is accomplished by means of an improved and more efficient Newton-Broydenmultidimensional root-finding algorithm. The explicit step relies on amultidimensional Riemann solver to compute the line-averaged electric andmagnetic fields at zone edges and it employs a one-dimensional Riemann solverat zone interfaces to update zone-centred hydrodynamic quantities. For thelatter, we introduce a five-wave solver based on the frozen limit of therelaxation system whereby the solution to the Riemann problem can be decomposedinto an outer Maxwell solver and an inner hydrodynamic solver. A number ofnumerical benchmarks demonstrate that our method is superior in stability androbustness to the more popular charge-conserving divergence cleaning approachwhere both primary electric and magnetic fields are zone-centered. In addition,the employment of a less diffusive Riemann solver noticeably improves theaccuracy of the computations.

A Constrained Transport Method for the Solution of the Resistive Relativistic MHD Equations