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We present the implementation of general-relativistic resistivemagnetohydrodynamics solvers and three divergence-free handling approachesadopted in the General-relativistic multigrid numerical (Gmunu) code.  In particular, implicit-explicit Runge-Kutta schemes are used to deal withthe stiff terms in the evolution equations for small resistivity.  Three divergence-free handling methods are (i) hyperbolic divergence cleaningthrough a generalised Lagrange multiplier (GLM); (ii) staggered-meshedconstrained transport (CT) schemes and (iii) elliptic cleaning though multigrid(MG) solver which is applicable in both cell-centred and face-centred (staggergrid) magnetic field.  The implementation has been test with a number of numerical benchmarks fromspecial-relativistic to general-relativistic cases.  We demonstrate that our code can robustly recover a very wide range ofresistivity.  We also illustrate the applications in modelling magnetised neutron stars,and compare how different divergence-free handling affects the evolution of thestars.  Furthermore, we show that the preservation of the divergence-free conditionof magnetic field when staggered-meshed constrained transport schemes can besignificantly improved by applying elliptic cleaning.

An extension of Gmunu: General-relativistic resistive magnetohydrodynamics based on staggered-meshed constrained transport with elliptic cleaning