A finite-difference method to be used in simulations of turbulence such as direct numerical simulation (DNS) and large-eddy simulation (LES) has been developed and verified in basic benchmark flows. The method is constructed using the general curvilinear coordinate system with the collocated grid arrangement of the variables so that it can be easily applied to various engineering flows including hydraulic applications involving complex geometry. The computer code is first verified by a test calculation of steady laminar flow in a curved cavity, then the same code is used in a DNS of fully-developed turbulent flow in a two-dimensional open channel. It is further used to conduct a LES simulation of the same flow. All the results indicate that the method is sound with sufficient accuracy for the intended applications.