On a momentum interpolation scheme for collocated meshes with improved discrete kinetic energy conservation

In this study, we investigate the effects of momentum interpolation (MI) schemes for collocated meshes on DNS and LES with relatively coarse meshes. Based on this, the primary objective is to present how a MI scheme with reduced errors in mass and discrete kinetic energy (DKE) conservation affects the quality of the simulation results. From an existing MI scheme used widely, it is shown that the continuity equation has a first-order error in time based on the CV-centered velocity. With a specific choice of the pressure variable of the order of the pressure change for interpolating the face velocity, we derive a MI scheme with temporally second-order for the continuity equation. It is noted that this scheme drives the continuity and DKE errors to zero for a steady flow or very small time step. When applied to DNS and LES of a turbulent channel flow and a turbulent flow around an airfoil, the suggested MI scheme with reduced error results in more accurate prediction of mean and RMS flow fields. In order to examine the effects of the MI schemes on the turbulent pressure field, energy and power spectra of pressure fluctuations are examined. The pressure spectra with the revised MI scheme show no clear sign of pressure wiggles at high frequencies and more accurate prediction of small-to-large scale fluctuations, which shows effectiveness of the revised scheme and importance of the mass and DKE conservation.