http://arxiv.org/abs/1603.01636
In the magnetosphere of a rotating black hole, an inner Alfven critical surface (IACS) must be crossed by inflowing plasma. Inside the IACS, Alfven waves are inward directed toward the black hole. The majority of the proper volume of the active region of spacetime (the ergosphere) is inside of the IACS. The charge and the totally transverse momentum flux (the momentum flux transverse to both the wave normal and the unperturbed magnetic field) are both determined exclusively by the Alfven polarization. However, numerical simulations of black hole magnetospheres are often based on 1-D HLL Riemann solvers that readily dissipate Alfven waves. Elements of the dissipated wave emerge in adjacent cells regardless of the IACS, there is no mechanism to prevent Alfvenic information from crossing outward. Thus, it is unclear how simulated magnetospheres attain the substantial Goldreich-Julian charge density associated with the rotating magnetic field. The HLL Riemann solver is also notorious for producing large recurring transients (i.e., it prevents a “well-balanced” numerical scheme), potentially masking the causal physical transients required to achieve a steady state. To overcome these shortcomings, we have formulated a one-dimensional Riemann solver, called HLLI, which incorporates the Alfven discontinuity and the contact discontinuity. We have also formulated a multidimensional Riemann solver, called MuSIC, that enables low dissipation propagation of Alfven waves in multiple dimensions. Such Riemann solvers also enable simulations that are well-balanced at least up to second order. The importance of higher order schemes in lowering the numerical dissipation of Alfven waves is also catalogued.
B. Punsly, D. Balsara, J. Kim, et. al.
Tue, 8 Mar 16
39/83
Comments: Submitted to ApJ