Large eddy simulation of flow through a periodic array of urban-like obstacles using a canopy stress method

Large-eddy simulation (LES) of a turbulent flow through an array of building-like obstacles is an idealized model to study transport of contaminants in the urban atmospheric boundary layer (urban ABL). A reasonably accurate LES prediction of turbulence in such an urban ABL must resolve a significant proportion of the small but energetic eddies in the roughness sublayer, which remains prohibitive even though computational power has been increased significantly. Recently, some researchers also reported a high level of inaccuracy in turbulence prediction if LES were coupled with an adaptive mesh refinement technique in order to optimize the cost of resolving the roughness sublayer. In this article, we present a turbulence closure methodology for LES of urban ABLs in which the roughness elements are represented through the canopy stress method, and the subgrid scale stress is modeled through a dynamically adaptive eddy viscosity method. Unlike the classical Smagorinsky model that considers only the 'strain portion' of the velocity gradient tensor, we consider both the 'strain tensor' and the 'rotation tensor' to compute the eddy viscosity. This allows us to dynamically adapt the rate of energy dissipation to the scale of the energetic eddies in the roughness sublayer. Without employing a mesh conforming to the urban roughness elements, the effect of such solid bodies are represented in the LES model through a canopy stress method in which the loss of pressure and the sink of momentum due to the interaction between eddies and roughness elements are parameterized using the instantaneous velocity field. Simulation results of the proposed canopy stress method is compared with that of a conventional Computational Fluid Dynamics (CFD) method employing a block-structured mesh conforming around the roughness elements. For urban flow simulations, the results demonstrate that the proposed canopy stress model is accurate in predicting vertical profiles of mean and variance, as well as the temporal intermittency of coherent structures.