Large eddy simulation for wind field analysis based on stabilized finite element method

In this paper, a stabilized large eddy simulation technique is developed to predict turbulent flow with high Reynolds number. Streamline Upwind Petrov-Galerkin (SUPG) stabilized method and three-step technique are both implemented for the finite element formulation of Smagorinsky sub-grid scale (SGS) model. Temporal discretization is performed using three-step technique with viscous term treated implicitly. And the pressure is computed from Poisson equation derived from the incompressible condition. Then two numerical examples of turbulent flow with high Reynolds number are discussed. One is lid driven flow at Re = <TEX>$10^5$</TEX> in a triangular cavity, the other is turbulent flow past a square cylinder at Re = 22000. Results show that the present technique can effectively suppress the instabilities of turbulent flow caused by traditional FEM and well predict the unsteady flow even with coarse mesh.

We propose and analyze a wall model based on the turbulent boundary layer equations (TBLE) for implicit large-eddy simulation (LES) of high Reynolds number wall-bounded flows in conjunction with a conservative immersed-interface method for mapping complex boundaries onto Cartesian meshes. Both implicit subgrid-scale model and immersed-interface treatment of boundaries offer high computational efficiency for complex flow configurations. The wall model operates directly on the Cartesian computational mesh without the need for a dual boundary-conforming mesh. The combination of wall model and implicit LES is investigated in detail for turbulent channel flow at friction Reynolds numbers from Re τ = 395 up to Re τ =100,000 on very coarse meshes. The TBLE wall model with implicit LES gives results of better quality than current explicit LES based on eddy viscosity subgrid-scale models with similar wall models. A straightforward formulation of the wall model performs well at moderately large Reynolds numbers. A logarithmic-layer mismatch, observed only at very large Reynolds numbers, is removed by introducing a new structure-based damping function. The performance of the overall approach is assessed for two generic configurations with flow separation: the backward-facing step at Re h = 5,000 and the periodic hill at Re H = 10,595 and Re H = 37,000 on very coarse meshes. The results confirm the observations made for the channel flow with respect to the good prediction quality and indicate that the combination of implicit LES, immersed-interface method, and TBLE-based wall modeling is a viable approach for simulating complex aerodynamic flows at high Reynolds numbers. They also reflect the limitations of TBLE-based wall models.

LES for pedestrian level wind around an idealized building array—Assessment of sensitivity to influencing parameters

A computational study of the standard large eddy simulation (LES) technique employing the dynamic Smagorinsky subgrid scale (SGS) model is compared to results using a highorder, implicit LES (ILES) technique with no SGS modeling. It has been shown in the past that ILES presents a viable substitute to the standard LES technique on canonical turbulent problems. The purpose of this paper is to evaluate the use of implicit LES with and without explicit subgrid scale models applied to problems of transitional ow over the SD7003 airfoil for various grid resolutions and Reynolds numbers. It will be shown that the addition of the SGS model does not oer a signicant advantage on coarser meshes when compared to the ILES approach. The ILES technique is shown to be an attractive alternative to SGS modeling in solution quality and computational cost and robustness for the ows examined.

Large eddy simulation of wind flow around dome structures by the finite element method

The separated turbulent flow past an inclined flat plate with sharp leading and trailing edges was computed based on three different simulation approaches for a reynolds number Rec= 20000 and a high angle of attack α=18°. The simulation techniques applied were the Reynolds‐averaged Navier–Stokes (RANS) equations combined with a one‐equation Spalart–Allmaras turbulence model, the large‐eddy simulation (LES) based on an algebraic eddy‐viscosity model, and a hybrid approach known as detached‐eddy simulation (DES) applying a slightly modified Spalart–Allmaras model in the entire integration domain. DES is a non‐zonal coupling technique of RANS and LES developed in the hope of reducing the large computational resources required for LES computations of turbulent flows with practical relevance. However, the objective of the present study was not to compare the resources (CPU time, memory) required for all three techniques but to investigate and evaluate the quality of the predicted results for RANS, DES and LES. For this purpose, a test case which is favourable to the basic concept of DES and which places special emphasis on the LES part of the DES concept was chosen. This last issue was important since the modified Spalart–Allmaras model applied as a subgrid scale model in the LES part is not as well validated as other models usually applied in LES. For this purpose, an LES prediction on a very fine grid served as a reference case for the evaluation. For all three techniques, predictions with different grid resolutions were carried out and compared with each other based on important integral parameters (e.g. Strouhal number, mean drag and lift coefficients and their standard deviations), the instantaneous and time‐averaged flow structures, and higher‐order statistics. As expected, the pure RANS calculation, although applied as unsteady RANS, failed to predict the unsteady characteristics of the separated flow. In contrast, the DES approach yielded reasonably the shedding phenomenon and some integral parameters. However, analysing the results in more detail led to remarkable deviations between the DES and LES predictions also when the same grid resolution was applied. Especially the free shear layer originating from the leading edge of the plate was not well reproduced by DES, showing strong deficiencies of the model applied as a subgrid scale model. The reasons for this behaviour of the model were analysed in detail. Two basic causes were identified; the first is given by some near‐wall corrections in the finite Reynolds number version of the model which are not working properly in the LES mode of DES. The second is a modified definition of the filter width typically applied for DES, leading to strongly increased values of the eddy viscosity. A revised version of the S–A model taking both issues seriously into account was used as a subgrid scale model in the LES mode. As a direct consequence, much better agreement with the reference LES solution was found for the DES prediction on the coarse grid, eliminating the deficiencies of the original formulation. Copyright© 2003 John Wiley &amp; Sons, Ltd.

The main objectives of this work are the formulation, implementation and applications of a numerical algorithm to simulate turbulent, incompressible, isothermal flows. The transient three-dimensional flow is analyzed using an explicit Taylor-Galerkin scheme and the finite element method with hexahedrical eight-node element. Turbulence is simulated using Large Eddy Simulation. For sub-grid scales two models were implemented, the classical Smagorinsky's model and the dynamic eddy viscosity model. For the second filtration, which is necessary in the dynamic model, a new method was developed based on independent finite elements that involve each node in the original mesh. The implemented scheme is efficient and good results with low additional computational cost were obtained. Results for two classical problems, the driven cavity and the backward facing step are presented. Comments about the model applicability for flows with high Reynolds numbers are also presented.

In this paper, the effect of subgrid-scale (SGS) modelling, grid resolution and anisotropy of the subgrid-scales on large eddy simulation (LES) is investigated. LES of turbulent channel flow is performed at Re τ=934, based on friction velocity and channel half width, for a wide range of resolutions. The dynamic Smagorinsky model (DS), the high-pass filtered dynamic Smagorinsky model (HPF) based on the variational multiscale method and the recent explicit algebraic model (EA), which accounts for the anisotropy of the SGS stresses are considered. The first part of the paper is focused on the resolution effects on LES, where the performances of the three SGS models at different resolutions are compared to direct numerical simulation (DNS) results. The results show that LES using eddy viscosity SGS models is very sensitive to resolution. At coarse resolutions, LES with the DS and the HPF models deviate considerably from DNS, whereas LES with the EA model still gives reasonable results. Further analysis shows that the two former models do not accurately predict the SGS dissipation near the wall, while the latter does, even at coarse resolutions. In the second part, the effect of SGS modelling on LES predictions of near-wall and outer-layer turbulent structures is discussed. It is found that different models predict near-wall turbulent structures of different sizes. Analysis of the spectra shows that although near-wall scales are not resolved at coarse resolutions, large-scale motions can be reasonably captured in LES using all the tested models.

The Discontinuous Galerkin (DG) method provides numerical solutions of the NavierStokes equations with high order of accuracy in complex geometries and allows for highly efficient parallelization algorithms. These attributes make the DG method highly attractive for large eddy simulation (LES). The main goal of this work is to investigate the feasibility of adopting an explicit filter to the numerical solution of the Navier-Stokes equations to increase the numerical stability of underresolved simulations such as LES and to use the explicit filter in dynamic subgrid scale (SGS) models for LES. The explicit filter takes advantage of DG’s framework where the solution is approximated using a polynomial basis. The higher modes of the solution correspond to a higher order polynomial basis, therefore by removing high order modes the filtered solution contains only lower frequency content. The explicit filter is successfully used here to remove the effects of aliasing in underresolved simulations of the Taylor-Green vortex case at a Reynolds number Re = 1600. The de-aliasing is achieved by evaluating a solution at a higher order polynomial (effectively increasing the number of quadrature points used for integration) and then projecting the solution down to a lower order polynomial. The SGS models investigated include the constant coefficient Smagorinsky Model (CCSM), Dynamic Smagorinsky Model (DSM), and Dynamic Heinz Model (DHM). The Taylor-Green Vortex case exhibits a laminar-turbulent transition and it is shown that the dynamic SGS models capture this transition more accurately than the CCSM when a sufficiently high polynomial order is used. The explicit test-filter operation for the dynamic models introduces a commutation error. A brief comparison of the effects of the commutative error that exists with this filter implementation is shown although further investigation is needed to determine the more appropriate order of operations.

The concept of dynamic large eddy simulation (LES) is highly attractive: such methods can dynamically adjust to changing flow conditions, which is known to be highly beneficial. For example, this avoids the use of empirical, case dependent approximations (like damping functions). Ideally, dynamic LES should be local in physical space (without involving artificial clipping parameters), and it should be stable for a wide range of simulation time steps, Reynolds numbers, and numerical schemes. These properties are not trivial, but dynamic LES suffers from such problems over decades. We address these questions by performing dynamic LES of periodic hill flow including separation at a high Reynolds number Re = 37 000. For the case considered, the main result of our studies is that it is possible to design LES that has the desired properties. It requires physical consistency: a PDF-realizable and stress-realizable LES model, which requires the inclusion of the turbulent kinetic energy in the LES calculation. LES models that do not honor such physical consistency can become unstable. We do not find support for the previous assumption that long-term correlations of negative dynamic model parameters are responsible for instability. Instead, we concluded that instability is caused by the stable spatial organization of significant unphysical states, which are represented by wall-type gradient streaks of the standard deviation of the dynamic model parameter. The applicability of our realizability stabilization to other dynamic models (including the dynamic Smagorinsky model) is discussed.

We apply the dynamic subgrid-scale model to a large-eddy simulation of turbulent channel flow with a square rib mounted on one wall. The Reynolds number Re is 3.21 x 10 3 based on the mean velocity above the obstacle and the obstacle's height. Near-wall structures are resolved with the no-slip boundary condition. The results show better agreement with direct numerical simulation than large-eddy simulation with a fixed model constant, verifying the value of the dynamic subgrid-scale model for simulating complex turbulent flows. ARGE-EDDY simulation (LES) is an accurate method of simulating complex turbulent flows in which the large flow structures are computed while small scales are modeled. The rationale behind this method is based on two observations: most of the turbulent energy is in the large structures, and the small scales are more isotropic and universal. Therefore, LES may be more general and less geometry dependent than Reynolds-averaged modeling, although it comes at higher cost. Even though LES has been used by many investigators, most research has been limited to flows with simple geometry. In engineering applications, however, one encounters more complicated geometries. Here we shall consider a rectangular parallelepiped mounted on a flat surface. Related flows are those over surfaces protruding from submarines (conning towers or control fins), wind flows around buildings, and airflows over computer chips, among others. The most distinctive features associated with these flows are three dimensionality, flow separation due to protruding surfaces, and large-scale unsteadiness. As a model flow, we consider a plane channel flow in which a two-dimensional obstacle is mounted on one surface (see Fig. 1). This relatively simple geometry contains flow separation and reattachment. Flow in this geometry has been studied by Tropea and Gackstatter1 for low Re and Werner and Wengle2 and Dimaczek et al.3 for high Re, among others. Recently, Germano et al. 4 suggested a dynamic subgridscale model (DSGSM) in which the model coefficient is dynamically computed as computation progresses rather than specified a priori. This approach is based on an algebraic identity between the subgrid-scale stresses at two different filter levels and the resolved turbulent stresses. They applied the model to transitional and fully turbulent channel flows and showed that the model contributes nothing in laminar flow and exhibits the correct asymptotic behavior in the nearwall region of turbulent flows without an ad hoc damping function. This is a significant improvement over conventional subgrid-scale modeling.

The moving finite element method with streamline-upwind Petrov–Galerkin for magnetohydrodynamic flows problems at high Hartmann numbers

Large eddy simulations and experiments on low-Reynolds-number laminar separation control for low-pressure turbine blades with oblong-dimpled surface

In the light of rapidly increasing applications of large-eddy-simulations (LES) it is deemed necessary to impose some quality assessment measures for such studies. The validation of LES is difficult because of the fact that both the sub-grid scale (sgs) model contribution and numerical discretization errors are functions of the grid resolution. In this study various index of quality measures, here and after referred to as LES_IQ, are proposed and applied to some case studies. The recommended LES_IQ is based on the concept of Richardson’s extrapolation. It is postulated that in practical applications of LES numerical dissipation will always be a significant part of the overall dissipation and it must be accounted for in any assessment of the quality of LES results. It is further suggested that an LES_IQ of 75% to 85% can be considered adequate for most engineering applications that typically occur at high Reynolds numbers; LES-IQ greater than 90% can be classified as DNS.

The near-wall, subgrid-scale (SGS) model [Chung and Pullin, Large-eddy simulation and wall-modeling of turbulent channel flow, J. Fluid Mech. 631, 281--309 (2009)] is used to perform large-eddy simulations (LES) of the incompressible developing, smooth-wall, flat-plate turbulent boundary layer. In this model, the stretched-vortex, SGS closure is utilized in conjunction with a tailored, near-wall model designed to incorporate anisotropic vorticity scales in the presence of the wall. The composite SGS-wall model is presently incorporated into a computer code suitable for the LES of developing flat-plate boundary layers. This is then used to study several aspects of zero- and adverse-pressure gradient turbulent boundary layers. First, LES of the zero-pressure gradient turbulent boundary layer are performed at Reynolds numbers Reθ based on the free-stream velocity and the momentum thickness in the range Reθ = 103 - 1012. Results include the inverse skin friction coefficient, √2/Cf, velocity profiles, the shape factor H, the Karman constant, and the Coles wake factor as functions of Reθ. Comparisons with some direct numerical simulation (DNS) and experiment are made, including turbulent intensity data from atmospheric-layer measurements at Reθ = O(106. At extremely large Reθ, the empirical Coles-Fernholz relation for skin-friction coefficient provides a reasonable representation of the LES predictions. While the present LES methodology cannot of itself probe the structure of the near-wall region, the present results show turbulence intensities that scale on the wall-friction velocity and on the Clauser length scale over almost all of the outer boundary layer. It is argued that the LES is suggestive of the asymptotic, infinite Reynolds-number limit for the smooth-wall turbulent boundary layer and different ways in which this limit can be approached are discussed. The maximum Reθ of the present simulations appears to be limited by machine precision and it is speculated, but not demonstrated, that even larger Reθ could be achieved with quad- or higher-precision arithmetic. Second, the time series velocity signals obtained from LES within the logarithmic region of the zero-pressure gradient turbulent boundary layer are used in combination with an empirical, predictive inner--outer wall model [Marusic et al., Predictive model for wall-bounded turbulent flow, Science 329, 193 (2010)] to calculate the statistics of the fluctuating streamwise velocity in the inner region of the zero-pressure gradient turbulent boundary layer. Results, including spectra and moments up to fourth order, are compared with equivalent predictions using experimental time series, as well as with direct experimental measurements at Reynolds numbers Reτ based on the friction velocity and the boundary layer thickness, Reτ =7,300, 13,600 and 19,000. LES combined with the wall model are then used to extend the inner-layer predictions to Reynolds numbers Reτ =62,000, 100,000 and 200,000 that lie within a gap in log(Reτ) space between laboratory measurements and surface-layer, atmospheric experiments. The present results support a log-like increase in the near-wall peak of the streamwise turbulence intensities with Reτ and also provide a means of extending LES results at large Reynolds numbers to the near-wall region of wall-bounded turbulent flows. Finally, we apply the wall model to LES of a turbulent boundary layer subject to an adverse pressure gradient. Computed statistics are found to be consistent with recent experiments and some Reynolds number similarity is observed over a range of two orders of magnitude.