p adé: A Code for Protoplanetary Disk Turbulence Based on Padé Differencing

Karim Shariff
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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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p adé:基于帕代差分法的原行星盘湍流代码
Padé 代码是为处理原行星盘中的流体动力湍流而开发的。它以圆柱坐标求解可压缩运动方程。与大多数天体物理学代码中使用的耗散冲击捕捉方案以及同阶的非扩散中央有限差分方案相比,该方案具有更高的分辨率。时间步进采用四阶 Runge-Kutta 方法。使用之前报告的误差校正 Fargo 方法来减少快速开普勒平流带来的时间步长限制。在需要捕捉冲击时,使用了人造体积粘度。对正确性和与处理器数量相关的扩展性进行了测试。最后,提出了提高效率和精度的建议。
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