High-order finite-difference method for incompressible flows using collocated grid system

Abstract

To apply the direct numerical simulation (DNS) and the large-eddy simulation (LES) of turbulence to flow fields of complicated geometry, a higher-order finite-difference method (FDM) has been developed for the body-fitted coordinate system. The consistency and the conservation property of FDMs are discussed for the collocated grid. As numerical examples, DNS results of decaying isotropic turbulence and DNS/LES results for plane channel flow are shown and the influence of variable arrangement is examined. The results by the consistent `interpolation' method for gradient form on the collocated grid agree well with those by other proper FDMs and the spectral method.