“…In addition to the aforementioned studies many numerical models that use the axisymmetric form of Navier-Stokes equations have been developed, for both compressible (Gokhale and Suresh, 1997; Clain et al , 2010; Musa et al , 2016) and incompressible (Leloudas et al , 2018, 2020; Saiac, 1990; Morsi et al , 1995; Durkish, 2006; Moshkin et al , 2010; Dağtekin and Ünsal, 2011; Lee and Lee, 2011; Semião and Carvalho, 1997) flows, featuring various discretization methods, flux evaluation schemes and turbulence models. Moreover, axisymmetric flow modelling has lately become a highly attractive topic in the context of mesoscopic approaches as well, such as the lattice Boltzmann method (LBM) (Zhang et al , 2019b; Lee et al , 2005; Huang et al , 2007; Liu et al , 2016; Li et al , 2018; Chen et al , 2019; Hajabdollahi et al , 2019; Liu et al , 2019). However, to the authors’ best knowledge, the implementation of an axisymmetric Navier-Stokes solver for swirling flows using the artificial compressibility method (ACM) is not available.…”