B LADES of small vertical-axis wind turbines operate at low Reynolds numbers and undergo continuous dynamic stall [1]. To improve the design of these blades, flow features such as separation and turbulent transition need to be captured accurately, which is still a challenge for most of the computational fluid dynamics codes. In a first attempt to simulate these flows, a code is developed and tested on a static airfoil at a low Reynolds number. When the chord Reynolds number Rec decreased below 500,000 the airfoil performance deteriorated by losing lift and increasing drag [2]. A free shear layer forms as the laminar boundary layer separates in an adverse pressure gradient forming a laminar separation bubble. This separated laminar boundary-layer transition to turbulence over an airfoil is a complex problem that is not completely understood. In particular, the information obtained so far is inadequate for clarifying the entire transition process, large-scale structures, and the instability mechanisms. Recently, an extensive experimental study of boundary-layer development for a NACA0025 airfoil at low Reynolds number was experimentally conducted [3]. Flow velocity datawere obtainedwith hot-wire anemometry.Wind-tunnel experiments were carried out for a range of Reynolds numbers from 10 to 10 and three angles of attack (5, 10, and 15 ). Two boundary-layer regimes were identified: 1) boundary-layer separation without reattachment and 2) separation bubble formation. Their results showed that transition to turbulence, which occurs because of the amplification of disturbances in the separated shear layer, plays a key role in boundary-layer reattachment. Their results also suggest that coherent structures form in the separated flow region and the formation of the roll-up vortices in the separated shear layer is linked to inviscid spatial growth of disturbances and is attributed to the Kelvin–Hemholtz instability. The final stage of transition is associated with the growth of a subharmonic component in the velocity spectrum, which can be attributed to the merging of the roll-up vortices. Given that the airfoil boundary layer at low Reynolds number is inherently unsteady and features important large-scale motions, this flow is not well predicted by Reynolds-averaged Navier–Stokes models. Instead a time-dependent simulation, such as a direct numerical simulation or large-eddy simulation (LES), is required for more accurate results. Large-eddy simulation is particularly suitable to investigate the generation and evolution of coherent structures in turbulent flows. It is ideal for low Reynolds number flows and explicit computation of coherent structures and has only limited sensitivity to modeling assumptions so that results are feasible for this practical problem. Flow past an experimentally studies NACA0025 airfoil is a challenging case for LES because of the different flow regimes around the airfoil, including the laminar boundary layer, laminar separation bubble, transition region, turbulent boundary layer, separation point, and separation region as well as wake region. In LES, it is important to resolve all important (large-scale) flow structures and model the remaining small-scale turbulence. Ideally, the goal would be to resolve the following flow regions: the laminar boundary layer with a sufficient amount of nodes (in the streamwise andwall-normal directions), the recirculation region (at the transition region and at the trailing edge), and the turbulent boundary layer. For blade design, it is also important to solve the flow in a short computational time. The code developed herein continues previous efforts to make LES applicable to complex flow simulations. The previous developed flow simulation methodology [4,5] also aims at obtaining accurate results on fewer grid nodes than standard LES. Although LES is promising, the drawback of LES is the large memory required if all the above mentioned regions are resolved. To control the size of the problem, an instantaneous wall function [6] is used, allowing the first nodes near the airfoil surface to be placed in the logarithm layer instead of in the sublayer. To further reduce computational cost, a pressure and velocity decoupled system is used. The consistent splitting method [7] evaluates the pressure by testing the momentum equation against gradients. The resulting Poisson equation for the pressure correction term avoids artificial boundary conditions. This scheme is free of splitting errors and the pressure error is smooth. Nonconforming finite elements with a lower requirement for degrees of freedom are chosen when compared to other conforming finite elements (e.g., the Taylor Hood element). This is a significant savings in memory and was suggested by [8] and implemented in FEATFLOW. Highly nonuniform meshes satisfy the resolution requirements of LES in the boundary layer. A traditional solver cannot damp the high frequencies generated by nonuniform meshes effectively, and a multigrid method is often needed. But the filtering operations on all the multigrid scales have to be separated from the traditional multigrid procedure to prevent errors between the different filtering scales. To get good LES results, a filtering operation is developed in the present work and discussed in Sec. II. In LES, the assumption of constant viscosity can not be made because of the eddy viscosity model used. This leads to a full coupling of the velocity components if an implicit treatment is applied for the viscous term. Two approaches have been traditionally used. One is the full coupled iterative method that can be solved iteratively but is expensive. The other is to treat the viscous term explicitly at the expense of reductions in the admissible time-step size due to stability restrictions. A third variable-viscosity formulation [9] can be used to discretize the variable-viscosity term.However, stability is not ensured because the variable-viscosity term is included on the right-hand side; in addition, this approach is computationally expensive. To simplify the above approach, a new scheme is adopted, where the variable viscosity is assumed piecewise constant in each element. Presented as Paper 4199 at the 18th AIAAComputational Fluid Dynamics Conference, Miami, FL, 25–28 June 2007; received 9 March 2009; accepted for publication 24 September 2009. Copyright © 2009 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved. Copies of this paper may be made for personal or internal use, on condition that the copier pay the $10.00 per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923; include the code 0021-8669/10 and $10.00 in correspondence with the CCC. ∗Department of Mechanical & Industrial Engineering; taoxu@mecheng1. uwaterloo.ca. Department of Mechanical & Industrial Engineering; sullivan@mie. utoronto.ca. Department of Mechanical & Industrial Engineering; paraschi@me. concordia.ca. JOURNAL OF AIRCRAFT Vol. 47, No. 1, January–February 2010