Analysis on Computational Efficiency of Convection Discretisation Schemes in SIMPLE Algorithm

Abstract

Computational Fluid Dynamics (CFD) is widely used to investigate heat transfer, fluid flow, chemical reaction and mass transfer phenomenon. While solving the Navier-Stokes equations, the convection term is always prone to numerical instability and therefore the discretisation of the convection term requires special attention. The performance of various convection schemes had been previously performed on one-dimensional convection-diffusion problem. Nevertheless, the numerical errors of these convection schemes are more pronounced in higher-dimensional problems especially those involving pressure term and flow recirculation. In this paper, the performances of convection schemes such as first order upwind differencing, second order upwind differencing, Quadratic Upstream Interpolation for Convective Kinematics (QUICK) and power-law schemes are investigated on the two-dimensional lid-driven flow problem in a square cavity. By using commercial CFD software ANSYS Fluent, the consistency, efficiency and accuracy of the results due to different convection schemes are compared. It is found that although the power-law scheme is the best in terms of iterative convergence rate, it is not accurate especially for high Re-flow. Higher order scheme such as QUICK is very accurate; however, its convergence rate is the lowest.