IMPLEMENTATION OF THE SHEARING BOX APPROXIMATION IN ATHENA

By James M. Stone, Thomas A. Gardiner. 2010

139 citations recorded by the source corpus.

We describe the implementation of the shearing box approximation for the study of the dynamics of accretion disks in the Athena magnetohydrodynamic (MHD) code. Second-order Crank–Nicholson time differencing is used for the Coriolis and tidal gravity source terms that appear in the momentum equation for accuracy and stability. We show that this approach conserves energy for epicyclic oscillations in hydrodynamic flows to round-off error. In the energy equation, the tidal gravity source terms are differenced as the gradient of an effective potential in a way that guarantees that total energy (including the gravitational potential energy) is also conserved to round-off error. We introduce an orbital advection algorithm for MHD based on constrained transport to preserve the divergence-free constraint on the magnetic field. This algorithm removes the orbital velocity from the time step constraint, and makes the truncation error more uniform in radial position. Modifications to the shearing box boundary conditions applied at the radial boundaries are necessary to conserve the total vertical magnetic flux. In principle, similar corrections are also required to conserve mass, momentum, and energy; however in practice we find that the orbital advection method conserves these quantities to better than 0.03% over hundreds of orbits. The algorithms have been applied to studies of the nonlinear regime of the MRI in very wide (up to 32 scale heights) horizontal domains.

Subfields: Astronomy and Astrophysics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/459e21268fc8e0cd87cde5c5dee5586958de4e3c

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Citations in the corpus

EFFECT OF AMBIPOLAR DIFFUSION ON THE NONLINEAR EVOLUTION OF MAGNETOROTATIONAL INSTABILITY IN WEAKLY IONIZED DISKS (2011, methodology): “Since the simulation is initialized from a turbulent state, the low level of stress and kinetic energy are mostly due to the eigen-modes of the shearing box excited from the initial turbulence, and that are not damped due to the low dissipation in the Athena code.”
THE MASS AND SIZE DISTRIBUTION OF PLANETESIMALS FORMED BY THE STREAMING INSTABILITY. I. THE ROLE OF SELF-GRAVITY (2015, methodology): “This is part of the orbital advection scheme (Stone & Gardiner 2010; Masset 2000; Johnson et al. 2008), which has been implemented for the gas dynamics as well.”
ASSESSING QUANTITATIVE RESULTS IN ACCRETION SIMULATIONS: FROM LOCAL TO GLOBAL (2011, methodology): “Previous comparisons between the Athena and Zeus simulations have indicated that Athena has lower turbulence decay rates for two-dimensional shearing sheet simulations compared to Zeus (Stone & Gardiner 2010; Stone 2009).”
TOWARD REALISTIC PROGENITORS OF CORE-COLLAPSE SUPERNOVAE (2011, methodology): “It is now possible to test these approximations by numerical simulation in both shearing box (Arnett & Meakin 2010; Stone & Gardiner 2010) and whole star domains (Brun & Palacios 2009; Brown et al. 2010); see also the theoretical developments of Balbus (2009) and Balbus & Weiss (2010).”
Three-phase Interstellar Medium in Galaxies Resolving Evolution with Star Formation and Supernova Feedback (TIGRESS): Algorithms, Fiducial Model, and Convergence (2016, methodology): “We solve the ideal MHD equations in a local, shearing box (e.g., Stone & Gardiner 2010).”
LOCAL STUDY OF ACCRETION DISKS WITH A STRONG VERTICAL MAGNETIC FIELD: MAGNETOROTATIONAL INSTABILITY AND DISK OUTFLOW (2012, methodology): “The shearing-box source terms (Coriolis force and tidal gravity) have been readily implemented in Athena (Stone & Gardiner 2010).”
WIND-DRIVEN ACCRETION IN PROTOPLANETARY DISKS. I. SUPPRESSION OF THE MAGNETOROTATIONAL INSTABILITY AND LAUNCHING OF THE MAGNETOCENTRIFUGAL WIND (2013, methodology): “Ohmic resistivity and AD have been implemented in Athena (Davis et al. 2010; Bai & Stone 2011).”
The Athena++ Adaptive Mesh Refinement Framework: Design and Magnetohydrodynamic Solvers (2020, methodology): “Subsequently, the code was augmented with different time integrators (Stone & Gardiner 2009), the shearing-box approximation (Stone & Gardiner 2010), cylindrical coordinates (Skinner & Ostriker 2010), special relativity (Beckwith & Stone 2011), particles (Bai & Stone 2010a), sink particles (Gong &…”
THREE-DIMENSIONAL HYDRODYNAMIC SIMULATIONS OF MULTIPHASE GALACTIC DISKS WITH STAR FORMATION FEEDBACK. I. REGULATION OF STAR FORMATION RATES (2013, methodology): “We utilize the Athena code with the van Leer integrator (Stone & Gardiner 2009), Roe’s Riemann solver, a piecewise linear spatial reconstruction scheme, and the orbital advection method for a shearing box (Stone & Gardiner 2010).”