Parametric Study of an Improved Gamma Differencing Scheme Based on Normalized-Variable Formulation for Low-Speed Flow With Artificial Compressibility Technique

Abstract

Based on the normalized-variable formulation (NVF), the modified GAMMA (MGAMMA) scheme previously devised for compressible flow calculations is now incorporated into an incompressible multigrid solver using the artificial compressibility (AC) technique on an unstructured grid. The MGAMMA scheme used in the present work is parameterized in order to further assess its accuracy and convergence compared to other well-known second-order high-resolution (HR) schemes, such as GAMMA and MINMOD. Testing is performed on three sets of problems: (1) advection of four scalar profiles; (2) flow in the Binnie-Green nozzle; and (3) flow past the NACA 0012 and NACA 4412 airfoils. It is shown that when lowering the diffusion-controlled parameter (β _m ), which serves as an attempt to reduce the numerical diffusion of the HR schemes tested, only the MGAMMA scheme is able to provide a converged solution while attaining solution accuracy.

Acknowledgments

This project is funded by the Ministry of Science Technology and Innovation (MOSTI), Malaysia, under IRPA Grant 09-99-03-0013-EA001 and UNITEN Internal Research Grant J510010026.