An efficient numerical method for RANS/LES turbulent simulations using subfilter scale stress transport equations

Abstract

SUMMARY We propose a numerical method for performing hybrid non-zonal RANS/LES simulations by using a subfilter scale stress transport model in the framework of finite volume technique. The turbulent equations are derived from the new partial integrated transport modeling (PITM) method. The PITM method has been initially developed for devising subfilter energy models based on the viscosity concept (Theoretical Computational Fluid Dynamics 2005; 18:443–468), and has been then extended to subfilter stress models relying on second-moment closures (Physics of Fluids 2005; 17(6); Int. J. Heat and Fluid Flow 2009; 30:602–616; Theoret. Comput. Fluid Dyn. 2007; 21(3):201–229.). The numerical method put in place is developed in a general framework of large eddy simulations and can be applied to almost all subfilter scale models based on transport equations of subfilter scale turbulent quantities. In this work, we have developed specific numerical schemes for solving the turbulent transport equations of compressible flows including the density, velocity, energy, subfilter scale turbulent stresses and subfilter scale dissipation rate that are strongly coupled together. When performing LES or VLES simulations, this coupling between the motion and turbulent equations poses some numerical problems because the subfilter scale turbulent stresses and dissipation rate are more fluctuating in time and space than in the case of RANS computations, so that a specific numerical treatment has been proposed. In this framework, new implicit iterative algorithms in time are especially developed for solving the unsteady equations of the turbulent energy, stresses and dissipation rate by ensuring the positivity of the normal stresses at each step of the computation. We show that the convective fluxes resulting from the volume technique including the main and turbulent variables can be computed by an approximate Riemann solver using new tensorial operators. The numerical solver is calibrated on the decay of isotropic spectrum and on the well-known fully turbulent channel flow for assessing the performances of the numerical method. Then, we perform numerical simulations of the turbulent channel flow over periodic hills on coarse and medium grids. This flow encountered in aeronautical applications is of complex physics as it is governed by interacting turbulence mechanisms associated with separation, recirculation and reattachment. As a result, it is found that the proposed numerical method used in conjunction with the subfilter stress model performs fairly well with these turbulent flows on different grids. From a practical point of view, this numerical method can be easily implemented in CFD codes for tackling engineering applications. Copyright © 2010 John Wiley & Sons, Ltd.