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

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‰-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.