A unified RANS–LES model: Computational development, accuracy and cost

Large eddy simulation (LES) is computationally extremely expensive for the investigation of wall-bounded turbulent flows at high Reynolds numbers. A way to reduce the computational cost of LES by orders of magnitude is to combine LES equations with Reynolds-averaged Navier–Stokes (RANS) equations used in the near-wall region. A large variety of such hybrid RANS–LES methods are currently in use such that there is the question of which hybrid RANS-LES method represents the optimal approach. The properties of an optimal hybrid RANS–LES model are formulated here by taking reference to fundamental properties of fluid flow equations. It is shown that unified RANS–LES models derived from an underlying stochastic turbulence model have the properties of optimal hybrid RANS–LES models. The rest of the paper is organized in two parts. First, a priori and a posteriori analyses of channel flow data are used to find the optimal computational formulation of the theoretically derived unified RANS–LES model and to show that this computational model, which is referred to as linear unified model (LUM), does also have all the properties of an optimal hybrid RANS–LES model. Second, a posteriori analyses of channel flow data are used to study the accuracy and cost features of the LUM. The following conclusions are obtained. (i) Compared to RANS, which require evidence for their predictions, the LUM has the significant advantage that the quality of predictions is relatively independent of the RANS model applied. (ii) Compared to LES, the significant advantage of the LUM is a cost reduction of high-Reynolds number simulations by a factor of 0.07 Re 0.46 . For coarse grids, the LUM has a significant accuracy advantage over corresponding LES. (iii) Compared to other usually applied hybrid RANS–LES models, it is shown that the LUM provides significantly improved predictions.