Second-order kinetic energy-conservative analysis of incompressible turbulence under a collocated grid system

Abstract

The study presented in this paper investigates the second-order conservation error of kinetic energy of an incompressible flow under a collocated grid. A collocated grid is often used to numerically analyse the flow around an aerofoil. The kinetic energy conservation error under a collocated grid is often greater than that under a staggered grid. The results of analysis based on coarse computational grids, such as LES analysis, are considerably affected by the kinetic energy conservation error. This study shows the results of numerical analysis in which the kinetic energy has a second-order conservation error under the collocated grid. This higher-order kinetic energy is strictly validated using inviscid flow. Furthermore, the results of conservation errors of higher-order statistics of kinetic energy are discussed in this study. The numerical analysis is then validated using a turbulent channel flow. The statistics obtained by this analysis agree well with those of previous studies in turbulent channel flows.