The Athena Astrophysical MHD Code in Cylindrical Geometry

TL;DR

This paper details the implementation of cylindrical coordinates in the Athena MHD code, enabling more accurate astrophysical simulations involving rotating disk systems while maintaining code simplicity and compatibility.

Contribution

The authors extend the Athena MHD code to cylindrical coordinates, preserving the original code structure and constrained transport, and validate it with a comprehensive test suite.

Findings

Successful implementation of cylindrical coordinates in Athena

Validation through standard and novel test problems

Code is suitable for diverse astrophysical applications

Abstract

A method for implementing cylindrical coordinates in the Athena magnetohydrodynamics (MHD) code is described. The extension follows the approach of Athena's original developers and has been designed to alter the existing Cartesian-coordinates code as minimally and transparently as possible. The numerical equations in cylindrical coordinates are formulated to maintain consistency with constrained transport, a central feature of the Athena algorithm, while making use of previously implemented code modules such as the Riemann solvers. Angular-momentum transport, which is critical in astrophysical disk systems dominated by rotation, is treated carefully. We describe modifications for cylindrical coordinates of the higher-order spatial reconstruction and characteristic evolution steps as well as the finite-volume and constrained transport updates. Finally, we present a test suite of standard and novel problems in one-, two-, and three-dimensions designed to validate our algorithms and implementation and to be of use to other code developers. The code is suitable for use in a wide variety of astrophysical applications and is freely available for download on the web.