A Compact Momentum Interpolation Procedure for Unsteady Flows and Relaxation

An improved version of the momentum interpolation approach for calculating velocities at the cell faces in nonstaggered grids is proposed. The procedure is developed for unsteady flows and takes into account the inclusion of relaxation. Regarding the integration in time, the first-order Euler and the second-order Euler and Adams-Moulton schemes are analyzed. The proposed procedure results in a compact, easy-to-implement expression which is shown to provide the desirable performance: Spurious oscillations of pressure are avoided; converged, steady solutions are independent from relaxation coefficient and time-step size; and the accuracy of the discretization is not negatively affected.