Unravelling cosmic velocity flows: a Helmholtz-Hodge decomposition algorithm for cosmological simulations

TL;DR

This paper introduces a Helmholtz-Hodge decomposition method for separating turbulent velocity fields into compressive and solenoidal components in cosmological simulations, achieving high accuracy across resolutions.

Contribution

The authors develop and implement a novel Helmholtz-Hodge decomposition algorithm tailored for multi-grid AMR cosmological simulation outputs, with demonstrated high accuracy.

Findings

Median errors around 1% in tests

Consistent accuracy across different resolutions

Effective decomposition around a galaxy cluster

Abstract

In the context of intra-cluster medium turbulence, it is essential to be able to split the turbulent velocity field in a compressive and a solenoidal component. We describe and implement a new method for this aim, i.e., performing a Helmholtz-Hodge decomposition, in multi-grid, multi-resolution descriptions, focusing on (but not being restricted to) the outputs of AMR cosmological simulations. The method is based on solving elliptic equations for a scalar and a vector potential, from which the compressive and the solenoidal velocity fields, respectively, are derived through differentiation. These equations are addressed using a combination of Fourier (for the base grid) and iterative (for the refinement grids) methods. We present several idealised tests for our implementation, reporting typical median errors in the order of $1\unicode{x2030}$-$1\%$, and with 95-percentile errors below a few percents. Additionally, we also apply the code to the outcomes of a cosmological simulation, achieving similar accuracy at all resolutions, even in the case of highly non-linear velocity fields. We finally take a closer look to the decomposition of the velocity field around a massive galaxy cluster.