A Conservative Pressure-Correction Method on Collocated Grid for Low Mach Number Flows

S. M. Yahya, S. F. Anwer, S. Sanghi

Department of Applied Mechanics, Indian Institute of Technology, Delhi, India.
Department of Mechanical Engineering, Zakir Husain College of Engineering & Technology, Aligarh Muslim University, Aligarh, India.

DOI: 10.4236/wjm.2012.25031                

Abstract

A novel extension to SMAC scheme is proposed for variable density flows under low Mach number approximation. The algorithm is based on a predictor—corrector time integration scheme that employs a projection method for the momentum equation. A constant-coefficient Poisson equation is solved for the pressure following both the predictor and corrector steps to satisfy the continuity equation at each time step. The proposed algorithm has second order centrally differenced convective fluxes with upwinding based on Cell Peclet number while diffusive flux are viscous fourth order accurate. Spatial discretization is performed on a collocated grid system that offers computational simplicity and straight forward extension to curvilinear coordinate systems. The algorithm is kinetic energy preserving. Further in this paper robustness and accuracy are demonstrated by performing test on channel flow with non-Boussinesq condition on different temperature ratios.

Keywords

LES; Non-Boussinesq; Low Mach Number; Turbulent Flow

Conflicts of Interest

The authors declare no conflicts of interest.

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