2010/06/01 by James M. Stone, Thomas A. Gardiner · 2 citations
Physics and Astronomy · #Advection #Angular momentum #Astrophysical Phenomena and Observations #Astrophysics and Star Formation Studies #Boundary (topology) #Magnetohydrodynamic drive #Magnetohydrodynamics #Nonlinear system #Scientific Research and Discoveries #Shearing (physics) #Tidal Model #astro-ph.IM
paper · pdf · doi:10.1088/0067-0049/189/1/142
18 pages, 11 figures. Accepted by ApJS
arxiv created 2010/06/01 · openalex publication_date 2010/06/23 · arxiv updated 2015/05/19 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.