A modulated gradient model for large-eddy simulation: Application to a neutral atmospheric boundary layer

Abstract

The subgrid-scale (SGS) parameterization represents a critical component of a successful large-eddy simulation (LES). It is known that in LES of high-Reynolds-number atmospheric boundary layer turbulence, standard eddy-viscosity models poorly predict mean shear in the near-wall region and yield erroneous velocity profiles. In this paper, a modulated gradient model is proposed. This approach is based on the Taylor expansion of the SGS stress, and uses local equilibrium hypothesis to evaluate the SGS kinetic energy. To ensure numerical stability, a clipping procedure is used to avoid local kinetic energy transfer from unresolved to resolved scales. Two approaches are considered to specify the model coefficient: a constant value of 1, and a simple correction to account for the effects of the clipping procedure on the SGS energy production rate. The model is assessed through a systematic comparison with well-established empirical formulations and theoretical predictions of a variety of flow statistics in a neutral atmospheric boundary layer. Overall, the statistics of the simulated velocity field obtained with the new model show good agreement with reference results and a significant improvement compared to simulations with standard eddy-viscosity models. For instance, the new model is capable to reproduce the expected log-law mean velocity profile and power-law energy spectra. Simulations also yield streaky structures and

Evaluation of subgrid-scale models in large-eddy simulation of flow past a two-dimensional block

“…In contrast, the modulated gradient model uses the gradient tensor (which can be obtained by Taylor's expansion of the SGS stress) to determine the structure (relative magnitude of the different components) of the SGS stress tensor. In simulations of a neutral atmospheric boundary layer flow, Lu and Porté-Agel (2010) demonstrated the better performance of the modulated gradient model in resolving the highly anisotropic near-surface flow compared with the results of the traditional Smagorinsky model. This is consistent with the current finding that the results of the modulated gradient model show the best overall agreement with the experimental data among the four SGS models tested.…”

“…As discussed in Lu and Porté-Agel (2010), the eddy-viscosity model uses a scalar eddy viscosity (the same value for all directions), which hinders its ability to account for strong flow anisotropy, especially on coarse grids. In contrast, the modulated gradient model uses the gradient tensor (which can be obtained by Taylor's expansion of the SGS stress) to determine the structure (relative magnitude of the different components) of the SGS stress tensor.…”

“…In this study, we test the performance of the Lagrangian scaledependent dynamic model (Porté-Agel et al, 2000;Stoll and Porté-Agel, 2006a) and the modulated gradient model (Lu and Porté-Agel, 2010) to study the flow past a two-dimensional (2D) block. This validation case is chosen because 2D block is commonly considered as an idealized building due to its simplicity in geometry, while still possessing the basic characteristics of a building block.…”

“…The other SGS model that is evaluated is the recently-developed modulated gradient model (Lu and Porté-Agel, 2010). In simulations of a neutral ABL, it is able to capture the most important statistical characteristics of boundary-layer turbulence.…”

“…The main advantages of the modulated gradient model are: (i) the model satisfies material frame indifference, (ii) it is simple and computationally inexpensive as no test filtering or additional transport equation is needed, and (iii) it is able to capture flow anisotropy better than eddy-viscosity models. As mentioned in Lu and Porté-Agel (2010), the eddy-viscosity closure assumes a one-to-one correlation between the SGS stress tensor and the strain rate tensor, and locally employs the same eddy-viscosity for all directions. This may be inaccurate and could induce errors when simulating strong anisotropic flows like the one considered here.…”