Turbulence Modeling Using Artificial Compressibility with Implicit LU-SGS Method

Abstract

A numerical method is developed to solve steady and unsteady incompressible turbulent flows in a curvilinear coordinate system on basis of [1]. The solution procedure is based on the method of artificial compressibility and uses a decoupled approach to solve the Reynolds-averaged Navier-Stokes(RANS)equations and k-ωturbulence model equations [2]. The third-order flux-difference splitting upwind differencing scheme, which is built to satisfy TVD condition, is used to discretize the convective terms in order to deal with the steep gradients existing in the k, ω fields. A time-accurate scheme for unsteady terms is achieved by using an implicit real time discretization and a dual-time approach, which introduces pseudo-unsteady terms into both RANS equations and k-ω model equations. An efficient implicit algorithm LU-SGS is developed for the pseudo-compressibility formulation of the incompressible RANS equations and turbulence model equations for both steady and unsteady flows. To validate the present method, numerical solutions for steady flows in a channel and in a circular tube with a severe constriction and for unsteady flow in a circular pipe are presented and compared with other numerical results or experimental data [3] [4].