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

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arxiv 2110.03732 v2 pith:PRXRHR4E submitted 2021-10-07 astro-ph.IM physics.comp-ph

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

Patrick Chi-Kit Cheong , David Yat Tung Pong , Anson Ka Long Yip , Tjonnie Guang Feng Li This is my paper
classification astro-ph.IM physics.comp-ph
keywords cleaningdivergence-freegeneral-relativisticconstrainedelliptichandlingschemesstaggered-meshed
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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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. Three divergence-free handling methods are (i) hyperbolic divergence cleaning through a generalised Lagrange multiplier (GLM); (ii) staggered-meshed constrained transport (CT) schemes and (iii) elliptic cleaning though multigrid (MG) solver which is applicable in both cell-centred and face-centred (stagger grid) magnetic field. The implementation has been test with a number of numerical benchmarks from special-relativistic to general-relativistic cases. We demonstrate that our code can robustly recover a very wide range of resistivity. We also illustrate the applications in modelling magnetised neutron stars, and compare how different divergence-free handling affects the evolution of the stars. Furthermore, we show that the preservation of the divergence-free condition of magnetic field when staggered-meshed constrained transport schemes can be significantly improved by applying elliptic cleaning.

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