Magnetohydrodynamics on an unstructured moving grid

Abstract

Magnetic fields play an important role in astrophysics on a wide variety of scales, ranging from the Sun and compact objects to galaxies and galaxy clusters. Here we discuss a novel implementation of ideal magnetohydrodynamics (MHD) in the moving mesh code AREPO which combines many of the advantages of Eulerian and Lagrangian methods in a single computational technique. The employed grid is defined as the Voronoi tessellation of a set of mesh-generating points which can move along with the flow, yielding an automatic adaptivity of the mesh and a substantial reduction of advection errors. Our scheme solves the MHD Riemann problem in the rest frame of the Voronoi interfaces using the HLLD Riemann solver. To satisfy the divergence constraint of the magnetic field in multiple dimensions, the Dedner divergence cleaning method is applied. In a set of standard test problems we show that the new code produces accurate results, and that the divergence of the magnetic field is kept sufficiently small to closely preserve the correct physical solution. We also apply the code to two first application problems, namely supersonic MHD turbulence and the spherical collapse of a magnetized cloud. We verify that the code is able to handle both problems well, demonstrating the applicability of this MHD version of AREPO to a wide range of problems in astrophysics.Comment: 11 pages, 9 figures, accepted by MNRA

A new class of accurate, mesh-free hydrodynamic simulation methods

“…However there is still significant noise. This comes from a combination of the "partition noise" above (a much milder form, compared to SPH, still exists in these methods, because our discrete volume partition estimator is only accurate to second-order; see § 2.7), as well as the usual "grid noise" associated with mesh motion/deformation (which can be significant here because, as discussed in § 2.6, the implicit deformation of the "effective faces" can be more complicated than simple uniform motion of a flat geometric face; see Springel 2011;McNally et al 2012;Muñoz et al 2014 for discussion of this noise in moving-mesh codes). We also find (not surprisingly) that the degree of vortex decay is very sensitive to our choice of slope-limiter: using a more conservative limit on monotonicity (see § B) leads to a smoother solution but much stronger damping of the vortex peak.…”

Galactic Winds Driven by Isotropic and Anisotropic Cosmic-Ray Diffusion in Disk Galaxies

“…Cooling and star formation are modeled as described in Springel & Hernquist (2003). Magnetic fields are modeled with ideal MHD using cell-centered magnetic fields and the Powell scheme (Powell et al 1999) for divergence control (Pakmor et al 2011;Pakmor & Springel 2013).…”

Stellar orbit evolution in close circumstellar disc encounters

“…Since a Voronoi tessellation changes continuously for smooth spatial trajectories of the generating points, each cell can be regarded as a "quasi-Lagrangian fluid parcel" (e.g., see Vogelsberger et al 2012). Besides ideal hydrodynamics coupled to self-gravity, the code currently includes routines for magneto-hydrodynamics (Pakmor, Bauer & Springel 2011;Pakmor & Springel 2013; see also Sales et al 2014), as well as numerous sub-resolution prescriptions for galaxy formation physics (Vogelsberger et al 2013). As in any unsplit, second-order, finite-volume method (see e.g., Toro 2009), the hyperbolic Euler equations are discretized for the i-th cell as (Springel 2010a):…”