A Multi-Scale, Multi-Domain Approach for LES of High Reynolds Number Wall-Bounded Turbulent Flows

Abstract

A major impediment to LES of high Reynolds number wall-bounded turbulent flows is the prohibitive resolution requirements of LES in the near-wall region. In the recent years, a number of wall modelling approaches have been proposed to bypass these resolution requirements (see [1] for a detailed review). Existing approaches are generally based on solving a reduced set of RANS equations in the near-wall region to obtain appropriate boundary conditions for LES, which is applied only in the outer layer of the flow. In application, these approaches have generally proved to be wanting in accuracy or scope [1]. In this study, we present a new multi-domain, multi-scale approach for LES of high Reynolds number wall-bounded turbulence. This approach capitalizes on the well-known quasi-periodicity of the turbulence structures in the near-wall region to solve the near-wall region in a minimal flow domain. This near-wall domain is then repeated periodically (or quasi-periodically) and matched to a full-domain LES in the core, solved at a much coarser resolution. This multi-scale approach has been implemented in LES of turbulent channel flow using a non-conforming, spectral domaindecomposition (patching) method. A schematic of the channel and the domains used in the nearwall and outer regions is shown in Fig. 1. Simulations have been performed for Re� � 1000, 2000, 5000, 10,000, and 20,000. The subgrid-scale model used in the simulations is the Nonlinear Interactions Approximations (NIA) model, recently developed in our group [2]. This model uses graded filters and deconvolution to directly model the nonlinear terms in the filtered Navier-Stokes equations, instead of the traditional subgrid-scale stresses. The NIA model has been shown to give very accurate predictions of both the filtered and full (filtered plus subgrid) turbulence statistics. In the multi-scale approach, the near-wall region is solved in a domain spanning the full length of the computational domain in the streamwise (x) direction, a height of 100 250 wall units in the wall-normal (z) direction, and a width of several hundred wall units in the spanwise (y) + +