Examining the Accuracy of Astrophysical Disk Simulations With a Generalized Hydrodynamical Test Problem

TL;DR

This paper introduces a generalized astrophysical disk test incorporating pressure and rotation, evaluating various SPH methods, and finds that CRKSPH significantly improves simulation accuracy over traditional SPH.

Contribution

It presents a new test problem for astrophysical disk simulations including pressure support and compares multiple SPH methods, highlighting CRKSPH's superior performance.

Findings

Traditional SPH performs poorly with pressure support, causing unphysical collapse.

CRKSPH substantially reduces errors in disk simulation.

Pressure support worsens traditional SPH accuracy.

Abstract

We discuss a generalization of the classic Keplerian disk test problem allowing for both pressure and rotational support, as a method of testing astrophysical codes incorporating both gravitation and hydrodynamics. We argue for the inclusion of pressure in rotating disk simulations on the grounds that realistic, astrophysical disks exhibit non-negligible pressure support. We then apply this test problem to examine the performance of various smoothed particle hydrodynamics (SPH) methods incorporating a number of improvements proposed over the years to help SPH better address problems noted in modeling the classical gravitation only Keplerian disk. We also apply this test to a newly developed extension of SPH based on reproducing kernels called CRKSPH. Counterintuitively, we find that pressure support worsens the performance of traditional SPH on this problem, causing unphysical collapse away from the steady-state disk solution even more rapidly than the purely gravitational problem, whereas CRKSPH greatly reduces this error.