Highly energy-conservative finite difference method for the cylindrical coordinate system

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Contribution of Reynolds stress distribution to the skin friction in wall-bounded flows (2002, methodology): “The data were obtained by DNS based on the energyconservative finite difference method [9] at the Reynolds number of Reb = 5300 (Reτu 180).”
A direct numerical simulation study on the mean velocity characteristics in turbulent pipe flow (2008, background): “Orlandi & Fatica (1997) and Fukagata & Kasagi (2002) simulated the same pipe flow as that of Eggels et al. with a second-order finite-difference method.”
A theoretical prediction of friction drag reduction in turbulent flow by superhydrophobic surfaces (2006, methodology): “The present DNS is performed using a second-order finite difference code, originally developed for pipe flow[11] and modified here to the Cartesian coordinates.”
Direct numerical simulation of spatially developing turbulent boundary layers with uniform blowing or suction (2011, methodology): “The DNS code is based on a channel flow code developed by Fukagata, Kasagi & Koumoutsakos (2006), which was itself adapted from a pipe flow code (Fukagata & Kasagi 2002).”
High order conservative finite difference scheme for variable density low Mach number turbulent flows (2007, methodology): “The results are compared with the latest DNS results by Fukagata and Kasagi [35] and the experimental measurements of Eggels et al.”