Simulation of three-dimensional incompressible viscous flows by DQ-SIMPLE algorithm

Abstract

In this study, DQ method is combined with SIMPLE strategy to solve the three-dimensional (3D) incompressible N-S equations in primitive variable formulation on a non-staggered grid. Three numerical approaches were proposed in this work, which are based on the pressure correction process with DQ discretization. The performance of three proposed approaches is comparatively studied by their application to simulate the 2D and 3D steady lid-driven cavity flows and the 2D unsteady lid-driven cavity flow. It was found that all of the three numerical approaches can generate very accurate numerical results by using a considerably small number of grid points, but Approach 1 is more competitive than Approaches 2 and 3 for solving both steady flow and unsteady flow problems. Our numerical Approach 1 was then applied to simulate several flow patterns of Couette-Taylor problem including Taylor vortex flow, wavy vortex flow and eccentric Taylor vortex flow.