The paper addresses the development of fully conservative finite difference schemes for incompressible flow simulations, focusing on both regular and staggered grid systems. The authors analyze the conservation properties of mass, momentum, and kinetic energy equations and derive schemes that satisfy these properties. They find that existing higher-order schemes for staggered grids do not conserve kinetic energy, and propose new fourth-order schemes that do. These schemes are validated through simulations of inviscid white noise in a two-dimensional periodic domain. The proposed schemes are also generalized to non-uniform grids and applied to large eddy simulations of turbulent channel flow, demonstrating their effectiveness and accuracy.The paper addresses the development of fully conservative finite difference schemes for incompressible flow simulations, focusing on both regular and staggered grid systems. The authors analyze the conservation properties of mass, momentum, and kinetic energy equations and derive schemes that satisfy these properties. They find that existing higher-order schemes for staggered grids do not conserve kinetic energy, and propose new fourth-order schemes that do. These schemes are validated through simulations of inviscid white noise in a two-dimensional periodic domain. The proposed schemes are also generalized to non-uniform grids and applied to large eddy simulations of turbulent channel flow, demonstrating their effectiveness and accuracy.