Anisotropic diffusion in mesh-free numerical magnetohydrodynamics

Abstract

We extend recently-developed mesh-free Lagrangian methods for numerical magnetohydrodynamics (MHD) to arbitrary anisotropic diffusion equations, including: passive scalar diffusion, Spitzer-Braginskii conduction and viscosity, cosmic ray diffusion/streaming, anisotropic radiation transport, non-ideal MHD (Ohmic resistivity, ambipolar diffusion, the Hall effect), and turbulent "eddy diffusion." We study these as implemented in the code GIZMO for both new meshless finite-volume Godunov schemes (MFM/MFV). We show the MFM/MFV methods are accurate and stable even with noisy fields and irregular particle arrangements, and recover the correct behavior even in arbitrarily anisotropic cases. They are competitive with state-of-the-art AMR/moving-mesh methods, and can correctly treat anisotropic diffusion-driven instabilities (e.g. the MTI and HBI, Hall MRI). We also develop a new scheme for stabilizing anisotropic tensor-valued fluxes with high-order gradient estimators and non-linear flux limiters, which is trivially generalized to AMR/moving-mesh codes. We also present applications of some of these improvements for SPH, in the form of a new integral-Godunov SPH formulation that adopts a moving-least squares gradient estimator and introduces a flux-limited Riemann problem between particles.

Simulating diverse instabilities of dust in magnetized gas

“…In addition to the generic code validation tests described in § 2, previous papers have extensively tested the numerical methods here (Carballido et al 2008;Johansen et al 2009;Bai & Stone 2010;Pan et al 2011;Hopkins & Raives 2016;Hopkins 2016bHopkins , 2017Su et al 2017;Hopkins & Lee 2016;Lee et al 2017;Moseley et al 2018;Seligman et al 2018). For example Hopkins & Lee (2016) show that the "finite-sampling" effects in super-particle methods, which introduce some shot noise in the particle densities and divergence between particle trajectories and gas (at the integration error level) in the perfectly-coupled limit (see Genel et al 2013), introduce ∼ 0.01 − 0.05 dex scatter in the dust density in a supersonically turbulent medium (δug/cs 1).…”

Braginskii viscosity on an unstructured, moving mesh accelerated with super-time-stepping

“…We consider a simulation inspired by the test problem in (Hopkins 2017). We take B = B(e x + e y )/ √ 2 with an initial velocity profile given by = cq(x)e y where…”

“…The best value for s max is likely to be problem dependent and we are not aware of a systematic approach to determining it. One potential idea, see the Appendix in Hopkins (2017), is to define a signal speed for the diffusive flux, diff , and use that to calculate the maximum super-time-step (and thereby s max ) as τ = C∆x/ diff at the beginning of each super-timestep. 2016).…”

Submillimetre Studies of Prestellar and Starless Cores in the Ophiuchus, Taurus and Cepheus Molecular Clouds

“…Hopkins (2012a) showed that the distribution of last-crossing structures matches the CMF, and can in some cases be reduced to the Hennebelle & Chabrier (2008) CMF model, while the mass spectrum, …”

“…Hennebelle & Chabrier (2008) used the Press-Schecter formalism to predict a CMF with a lognormal distribution at low masses, and a Salpeter power law at high masses, with the change in behaviour occuring at the mass at which the local Jeans mass is exceeded. This work has been extended by Hopkins (2012a) and Hopkins (2012b), who reconstructed the CMF from a rotationally-supported turbulent Galactic disc.…”