Computational study of incompressible turbulent flows with method of characteristics

Turbulent flows are the most applicable cases that in recent years the researches have been focused on developing of solution methods. Incompressible turbulent flow is one of these cases which need to be taken in account. Solving the incompressible Navier-stokes equation because of elliptical characteristics has been led to some researches in this field recently. The ACM of Chorin [1] as a pre-conditioner enables the coupling of continuity and momentum equations thus allowing time marching compressible schemes to be applied for incompressible ones. The CB methods for ACM, was proposed by Drikakis et al. [2] based on the definition of primitive variables as functions of their values on the characteristics and formation of compatibility equations. Razavi and Atashbar extended Roe scheme to estimate convective fluxes of incompressible viscous flows past a hydrofoil. This method is based on the propagations of virtual acoustic waves which enables damping the numerical oscillations [3]. Nithiarasu and Liu [4] implemented artificial compressibility to solve incompressible turbulent flows at medium Reynolds numbers with characteristic-based scheme. They used three different turbulence models namely Wolfenstein model, Spalart-Allmaras model and standard   k model. Finite volume method along with hybrid grid and   k turbulence model was proposed by Feng and Shanhang [5]. Yang and Chang [6] used 2D numerical simulation of turbulent flow fields for NREL S809 airfoil. In addition LES is the other field of turbulence modeling which Catalano et al. [7] proposed a LES model to simulate flows past a circular cylinder in supercritical regime by finite deference method. In this study, a finite volume model is presented for solving incompressible turbulent flows past a circular cylinder. Considering Spalart-Allmaras as a turbulence model CB method is used in formulations. The behavior and performance of Spalart-Allmaras turbulence model is investigated. The numerical results are obtained and validated by other available results in the literature.