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P ADÉ: A Code for Protoplanetary Disk Turbulence Based on Padé Differencing

Authors

Shariff, Karim
RefereedArticle

Abstract

The PADÉ code has been developed to treat hydrodynamic turbulence in protoplanetary disks. It solves the compressible equations of motion in cylindrical coordinates. Derivatives are computed using nondiffusive and conservative fourth-order Padé differencing, which has higher resolving power compared to both dissipative shock-capturing schemes used in most astrophysics codes, as well as nondiffusive central finite-difference schemes of the same order. The fourth-order Runge–Kutta method is used for time stepping. A previously reported error-corrected Fargo approach is used to reduce the time step constraint imposed by rapid Keplerian advection. Artificial bulk viscosity is used when shock capturing is required. Tests for correctness and scaling with respect to the number of processors are presented. Finally, efforts to improve efficiency and accuracy are suggested.

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*The material contained in this document is based upon work supported by a National Aeronautics and Space Administration (NASA) grant or cooperative agreement. Any opinions, findings, conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect the views of NASA.

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