Vortex-p: a Helmholtz-Hodge and Reynolds decomposition algorithm for particle-based simulations

TL;DR

Vortex-p is a new algorithm and tool designed to perform Helmholtz-Hodge and Reynolds decompositions on velocity fields from particle-based simulations, enabling detailed turbulence analysis in complex astrophysical flows.

Contribution

The paper introduces vortex-p, a novel, publicly available algorithm that efficiently computes decompositions on non-uniform, particle-based simulation data using adaptive mesh refinement and iterative filtering.

Findings

Accurate and scalable decompositions demonstrated on idealised tests.

Effective application to galaxy cluster simulations with various physics.

Vortex-p outperforms traditional methods on non-uniform data.

Abstract

Astrophysical turbulent flows display an intrinsically multi-scale nature, making their numerical simulation and the subsequent analyses of simulated data a complex problem. In particular, two fundamental steps in the study of turbulent velocity fields are the Helmholtz-Hodge decomposition (compressive+solenoidal; HHD) and the Reynolds decomposition (bulk+turbulent; RD). These problems are relatively simple to perform numerically for uniformly-sampled data, such as the one emerging from Eulerian, fix-grid simulations; but their computation is remarkably more complex in the case of non-uniformly sampled data, such as the one stemming from particle-based or meshless simulations. In this paper, we describe, implement and test vortex-p, a publicly available tool evolved from the vortex code, to perform both these decompositions upon the velocity fields of particle-based simulations, either from smoothed particle hydrodynamics (SPH), moving-mesh or meshless codes. The algorithm relies on the creation of an ad-hoc adaptive mesh refinement (AMR) set of grids, on which the input velocity field is represented. HHD is then addressed by means of elliptic solvers, while for the RD we adapt an iterative, multi-scale filter. We perform a series of idealised tests to assess the accuracy, convergence and scaling of the code. Finally, we present some applications of the code to various SPH and meshless finite-mass (MFM) simulations of galaxy clusters performed with OpenGadget3, with different resolutions and physics, to showcase the capabilities of the code.