Local Simulations of MRI turbulence with Meshless Methods

Abstract

The magneto-rotational instability (MRI) is one of the most important processes in sufficiently ionized astrophysical disks. Grid-based simulations, especially those using the local shearing box approximation, provide a powerful tool to study the nonlinear turbulence the MRI produces. On the other hand, meshless methods have been widely used in cosmology, galactic dynamics, and planet formation, but have not been fully deployed on the MRI problem. We present local unstratified and vertically stratified MRI simulations with two meshless MHD schemes: a recent implementation of SPH MHD (Price 2012), and a MFM MHD scheme with constrained gradient divergence cleaning, as implemented in the GIZMO code (Hopkins 2017). Concerning variants of the SPH hydro force formulation, we consider both the "vanilla" SPH and the PSPH variant included in GIZMO. We find, as expected, that the numerical noise inherent in these schemes affects turbulence significantly. Also a high-order kernel, free of the pairing instability, is necessary. Both schemes adequately simulate MRI turbulence in unstratified shearing boxes with net vertical flux. The turbulence, however, dies out in zero-net-flux unstratified boxes, probably due to excessive numerical dissipation. In zero-netflux vertically stratified simulations, MFM can reproduce the MRI dynamo and its characteristic butterfly diagram for several tens of orbits before ultimately decaying. In contrast, extremely strong toroidal fields, as opposed to sustained turbulence, develop in equivalent simulations using SPH MHD. The latter unphysical state is likely caused by a combination of excessive artificial viscosity, numerical resistivity, and the relatively large residual errors in the divergence of the magnetic field.

Global Simulations of Self-gravitating Magnetized Protoplanetary Disks

“…MRI-hr has a weaker Maxwell stress than both grvmhd1 and grvmhd2, which reflects the weaker amplification of the magnetic field relative to the runs in which the dynamo operates. We also note that, α M = 2 M rφ / B 2 ∼ 0.4 in MRI-hr, this being characteristic of resolved MRI simulations (Parkin & Bicknell 2013;Hawley et al 2011;Deng et al 2019).…”

“…Flock et al 2011). The reproduction of this generic feature of the MRI dynamo gives us some confidence that our global simulations can describe the MRI up to some level of accuracy for some period of time (see also Deng et al 2019).…”

“…It must be conceded from the outset that the weak field limit, in particular, is polluted (as in all particle codes) by small-scale (resolution dependent) noise, arising from insufficient div(B) cleaning (Deng et al 2019). Throughout our simulations the domain averaged dimensionless divergence |h * ∇ · B/B| is kept to ∼ 10 −3 , where the angle brackets indicates a domain average and h is the resolution length (Deng et al 2019). But despite this relatively low value, the persistent deviation from solenoidality introduces an artificial magnetic diffusion and low-level magnetic activity on the smallest scales.…”

“…But despite this relatively low value, the persistent deviation from solenoidality introduces an artificial magnetic diffusion and low-level magnetic activity on the smallest scales. This additional numerical diffusivity may explain some of the decaying MRI behaviour witnessed in Deng et al (2019); it also makes challenging the simulation of weak fields, and the estimation of (kinematic) dynamo growth rates. We hence limit ourselves to stronger field initialisations, and keep in mind the enhanced numerical resistivity exhibited by these simulations.…”

Formation of the First Stars and Black Holes

“…The angular momentum barrier is thus particularly strong for SMSs. Two mechanisms might allow for efficient angular momentum loss in the accretion process: gravitational torques (Begelman et al, 2006;Wise et al, 2008; and magnetic fields (Pandey et al, 2019;Deng et al, 2019Deng et al, , 2020. Supermassive accretion discs are highly gravitationally unstable, and departures from axial symmetry are pronounced.…”