Preconditioning Based on a Partially Implicit Implementation of Momentum Interpolation for Coupled Solvers

A new implicit and coupled algorithm for solving the Navier-Stokes equations is presented. A discretized Poisson-like equation for pressure is derived from the continuity equation by using expressions for the face velocities corrected with the momentum interpolation approach. A partially implicit implementation of this equation is proposed in order to achieve the coupling of velocity and pressure without increasing the size of the computational molecule. The ability of the algorithm to solve both constant- and variable-density flows is shown by presenting numerical results for the lid-driven cavity flow at moderate and high Reynolds numbers, and for the buoyancy-driven cavity flow with large temperature differences. A fully implicit scheme is used for discretizing the transient terms, and the efficiency and accuracy of the algorithm for unsteady flows is shown by solving the laminar vortex shedding over a square cylinder.