Pade: A code for protoplanetary disk turbulence based on Pade differencing

TL;DR

The Pade code offers a high-resolution, conservative method for simulating hydrodynamic turbulence in protoplanetary disks, improving accuracy over traditional schemes through Pade differencing and optimized time stepping.

Contribution

It introduces a novel Pade differencing scheme for hydrodynamics in protoplanetary disks, enhancing resolution and efficiency compared to existing methods.

Findings

Demonstrates higher resolving power than shock-capturing schemes

Shows good scalability with processor number

Provides accurate turbulence simulations in protoplanetary disks

Abstract

The Pade 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 non-diffusive and conservative fourth-order Pade differencing, which has higher resolving power compared to both dissipative shock-capturing schemes used in most astrophysics codes, as well as non-diffusive 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.