Conservation properties of vectorial operator splitting

This work is concerned with the conservation properties of a new vectorial operator splitting scheme for solving the incompressible Navier–Stokes equations. It is proven that the difference approximation of the advection operator conserves square of velocity components and the kinetic energy as the differential operator does, while pressure term conserves only the kinetic energy. Some analytical requirements necessary to be satisfied of difference schemes for incompressible Navier–Stokes equations are formulated and discussed. The properties of the methods are illustrated with results from numerical computations for lid-driven cavity flow.