A Vorticity-Preserving Hydrodynamical Scheme for Modeling Accretion Disk Flows

TL;DR

This paper introduces a vorticity-preserving hydrodynamical scheme for simulating complex astrophysical disk flows, demonstrating its accuracy and potential advantages over traditional methods in modeling vortex dynamics.

Contribution

It presents a second-order accurate, vorticity-preserving implicit scheme for compressible flows, with validation against other common astrophysical simulation algorithms.

Findings

Lerat et al.'s scheme accurately conserves vorticity in inviscid flows.

The scheme outperforms some traditional methods in vortex-rich flow simulations.

It is particularly useful for environments where vortex dynamics are critical.

Abstract

Vortices, turbulence, and unsteady non-laminar flows are likely both prominent and dynamically important features of astrophysical disks. Such strongly nonlinear phenomena are often difficult, however, to simulate accurately, and are generally amenable to analytic treatment only in idealized form. In this paper, we explore the evolution of compressible two-dimensional flows using an implicit dual-time hydrodynamical scheme that strictly conserves vorticity (if applied to simulate inviscid flows for which Kelvin's Circulation Theorem is applicable). The algorithm is based on the work of Lerat, Falissard & Side (2007), who proposed it in the context of terrestrial applications such as the blade-vortex interactions generated by helicopter rotors. We present several tests of Lerat et al.'s vorticity-preserving approach, which we have implemented to second-order accuracy, providing side-by-side comparisons with other algorithms that are frequently used in protostellar disk simulations. The comparison codes include one based on explicit, second-order van-Leer advection, one based on spectral methods, and another that implements a higher-order Godunov solver. Our results suggest that Lerat et al's algorithm will be useful for simulations of astrophysical environments in which vortices play a dynamical role, and where strong shocks are not expected.