An Extension of Gmunu: General-relativistic Resistive Magnetohydrodynamics Based on Staggered-meshed Constrained Transport with Elliptic Cleaning

Abstract

We present the implementation of general-relativistic resistive magnetohydrodynamics solvers and three divergence-free handling approaches adopted in the General-relativistic multigrid numerical (Gmunu) code. In particular, implicit–explicit Runge–Kutta schemes are used to deal with the stiff terms in the evolution equations for small resistivity. The three divergence-free handling methods are (i) hyperbolic divergence cleaning (also known as the generalized Lagrange multiplier), (ii) staggered-meshed constrained transport schemes, and (iii) elliptic cleaning through a multigrid solver, which is applicable in both cell-centered and face-centered (stagger grid) magnetic fields. The implementation has been tested with a number of numerical benchmarks from special-relativistic to general-relativistic cases. We demonstrate that our code can robustly recover from the ideal magnetohydrodynamics limit to a highly resistive limit. We also illustrate the applications in modeling magnetized neutron stars, and compare how different divergence-free handling methods affect the evolution of the stars. Furthermore, we show that the preservation of the divergence-free condition of the magnetic field when using staggered-meshed constrained transport schemes can be significantly improved by applying elliptic cleaning.

General-relativistic Radiation Transport Scheme in Gmunu. I. Implementation of Two-moment-based Multifrequency Radiative Transfer and Code Tests

“…where the i  here is for the covariant derivatives associated with the reference metric ij ĝ . As in our previous work (Cheong et al 2021(Cheong et al , 2022H. H.-Y.…”

“…The radiation fields contribute to the total energy-momentum tensor, which affects the hydrodynamical and metric equations. The hydrodynamical evolution equations are essentially the same as those in Cheong et al (2021Cheong et al ( , 2022, except that the radiation four-force also arises in the source terms of energy and momentum equations, namely as follows:…”

“…The radiation-matter interaction terms are solved implicitly since they are very stiff in the optically thick region. As in our previous work (Cheong et al 2022), we adopt the implicit-explicit (IMEX) Runge-Kutta time integrators (see, e.g., Ascher et al 1997;Pareschi & Russo 2005) to implicitly handle the stiff source terms while keeping the time step reasonable. These schemes have been applied and tested in several radiation hydrodynamics codes (e.g., Weih et al 2020b;Anninos & Fragile 2020;Laiu et al 2021;Izquierdo et al 2023).…”

Oscillations of highly magnetized non-rotating neutron stars

“…Simulations. Simulations are performed with our code Gmunu [75][76][77][78] . For each of the 12 equilibrium models, we execute Gmunu three times, once for each initial perturbation function.…”

“…A more rigorous approach to compute strongly magnetized equilibrium models is recently presented and demonstrated by an opensource code XNS 3,[64][65][66][67][68][69][70][71][72][73][74] . Moreover, the GRMHD code Gmunu [75][76][77][78] allows us to robustly evolve NSs in dynamical spacetime even with extreme magnetic fields of 10 15−17 G. With these powerful tools in hand, we are now in a much better position to systematically investigate the oscillation modes of magnetized NSs.…”