Mathematical Problems in Engineering
Volume 2011 (2011), Article ID 712372, 20 pages
Research Article

Finite Element Analysis of Turbulent Flows Using LES and Dynamic Subgrid-Scale Models in Complex Geometries

1Department of Engineering Mechanics, Kunming University of Science and Technology, Yunnan, Kunming 650051, China
2School of Engineering, University of Aberdeen, Aberdeen AB24 3UE, UK

Received 24 January 2011; Revised 24 April 2011; Accepted 25 May 2011

Academic Editor: Sergio Preidikman

Copyright © 2011 Wang Wenquan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


An innovative computational model is presented for the large eddy simulation (LES) of multidimensional unsteady turbulent flow problems in complex geometries. The main objectives of this research are to know more about the structure of turbulent flows, to identify their three-dimensional characteristic, and to study physical effects due to complex fluid flow. The filtered Navier-Stokes equations are used to simulate large scales; however, they are supplemented by dynamic subgrid-scale (DSGS) models to simulate the energy transfer from large scales toward subgrid-scales, where this energy will be dissipated by molecular viscosity. Based on the Taylor-Galerkin schemes for the convection-diffusion problems, this model is implemented in a three-dimensional finite element code using a three-step finite element method (FEM). Turbulent channel flow and flow over a backward-facing step are considered as a benchmark for validating the methodology by comparing with the direct numerical simulation (DNS) results or experimental data. Also, qualitative and quantitative aspects of three-dimensional complex turbulent flow in a strong 3D blade passage of a Francis turbine are analyzed.