A constrained transport method for the solution of the resistive relativistic MHD equations Article Swipe
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· 2019
· Open Access
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· DOI: https://doi.org/10.1093/mnras/stz1015
· OA: W2933257122
We describe a novel Godunov-type numerical method for solving the equations\nof resistive relativistic magnetohydrodynamics. In the proposed approach, the\nspatial components of both magnetic and electric fields are located at zone\ninterfaces and are evolved using the constrained transport formalism. Direct\napplication of Stokes' theorem to Faraday's and Ampere's laws ensures that the\nresulting discretization is divergence-free for the magnetic field and\ncharge-conserving for the electric field. Hydrodynamic variables retain,\ninstead, the usual zone-centred representation commonly adopted in\nfinite-volume schemes. Temporal discretization is based on Runge-Kutta\nimplicit-explicit (IMEX) schemes in order to resolve the temporal scale\ndisparity introduced by the stiff source term in Ampere's law. The implicit\nstep is accomplished by means of an improved and more efficient Newton-Broyden\nmultidimensional root-finding algorithm. The explicit step relies on a\nmultidimensional Riemann solver to compute the line-averaged electric and\nmagnetic fields at zone edges and it employs a one-dimensional Riemann solver\nat zone interfaces to update zone-centred hydrodynamic quantities. For the\nlatter, we introduce a five-wave solver based on the frozen limit of the\nrelaxation system whereby the solution to the Riemann problem can be decomposed\ninto an outer Maxwell solver and an inner hydrodynamic solver. A number of\nnumerical benchmarks demonstrate that our method is superior in stability and\nrobustness to the more popular charge-conserving divergence cleaning approach\nwhere both primary electric and magnetic fields are zone-centered. In addition,\nthe employment of a less diffusive Riemann solver noticeably improves the\naccuracy of the computations.\n
