An Explicit Pressure-Based Algorithm for Incompressible Flows

Abstract

A new solution procedure called Diagonal Split Corrected Linked Equations via Operator splitting (DS-CLEO) has been developed for solving the momentum equations in the pressure-based SIMPLER-type formulation of the incompressible Navier-Stokes equations. An explicit momentum predictor step based on a time splitting procedure is shown to possess unconditional stability while only the implicit pressure equation requires a computationally intensive iterative solver. No relaxation of any of the governing equations is necessary to ensure convergence for either steady or unsteady problems. It is demonstrated that pressure-velocity coupling and second order time accuracy is obtained through a set of inner iterations on the pressure and velocity fields using the exact discretized equations. The Diagonal Split procedure offered a 33.9 and 35.9x reduction in runtime compared to SIMPLER for two unsteady problems tested and a minor runtime reduction for steady lid-driven cavity flow.