# Implementation of the Shearing Box Approximation in Athena

@article{Stone2010ImplementationOT, title={Implementation of the Shearing Box Approximation in Athena}, author={James M. Stone and Thomas A. Gardiner}, journal={Astrophysical Journal Supplement Series}, year={2010}, volume={189}, pages={142-155} }

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… Expand

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