Code

Large-eddy simulation toolbox ‘lesTools’

lesTools is a toolbox of MATLAB scripts that can aid in the construction and assessment of subgrid-scale models for large-eddy simulations of turbulent flows.

Currently, lesTools consists of two modules. The first module can be used to study the statistical behavior of physical quantities that are based on the velocity gradient of turbulent flows. The second module can be used to study the near-wall scaling behavior of quantities that are based on the velocity field of incompressible turbulent flows.

Flow statistics

Background

Large-eddy simulation is a powerful methodology for the numerical prediction of the behavior of turbulent flows. In large-eddy simulation, the large scales of motion in flows are explicitly computed, whereas the effects of the small-scale motions are modeled using subgrid-scale models (see, e.g., the monographs by Sagaut [1] and Pope [2]). Most subgrid-scale models can, however, only be used in a practical large-eddy simulation, once the value of one or more model constants has been determined.

The model constants of eddy viscosity models can be estimated using a simple dissipation argument. One requires that the average subgrid dissipation due to an eddy viscosity model matches the average dissipation of the Smagorinsky model [3, 4, 5, 6]. The average subgrid dissipation of a subgrid-scale model can, for example, be computed using the velocity field of a homogeneous isotropic turbulent flow, either coming from an experiment or a numerical simulation [3]. Alternatively, the subgrid dissipation can be estimated using a large number of synthetic velocity gradients, given by random matrices [4, 5] that may be sampled from a uniform distribution [6]. One subsequently equates the average subgrid dissipation from the eddy viscosity model of interest with the average dissipation of the Smagorinsky model to obtain an estimate of the sought model constant in terms of the Smagorinsky constant.

The above dissipation estimate cannot be used to determine the model constant of subgrid-scale model terms that are nondissipative. Consider, for example, nonlinear terms that are proportional to the commutator of the rate-of-strain and rate-of-rotation tensors [7, 8]. We can, however, determine the desired order of magnitude of the model constant of such a nonlinear term as follows [8]. We first determine the average value of the coefficient that accompanies the nonlinear term. To obtain an estimate of the model constant of the nonlinear term, we then compare this average with the proportionality constant of 1 / 12 of the same nonlinear term in the gradient model, which forms the lowest-order Taylor series approximation of the turbulent stress tensor in terms of the filter length.

Module

The flowStats module of lesTools provides scripts that facilitate the determination of the statistical behavior of physical quantities that are based on the velocity gradient of turbulent flows. In particular, this module can be used to determine the average dissipation and the average model coefficients of subgrid-scale models. We can, thus, use this module to estimate the model constants of subgrid-scale models for large-eddy simulation [6, 7, 8].

Usage

Usage of the MATLAB scripts of the flowStats module is explained in detail in the readme in the flowStats folder of this toolbox.

Depending on your purposes, please consider citing the work by Silvis et al. [6] and/or Silvis et al. [8] when making use of the flowStats module.

Acknowledgments

Mirko Signorelli is kindly acknowledged for his assistance in determining the accuracy of the flow statistics.

Near-wall scaling behavior

Background

Using numerical simulations, Chapman and Kuhn [9] revealed the limiting power-law behavior of incompressible turbulence near a solid wall. Among other things, they determined the scaling behavior of the Reynolds stresses in terms of the wall-normal distance. To ensure that, for example, the dissipation of kinetic energy near solid walls is properly captured, subgrid-scale models for the turbulent stresses should exhibit the same asymptotic near-wall behavior as the Reynolds stresses [4, 5, 6, 7].

The near-wall behavior of subgrid-scale models can be studied by expanding the components of the velocity field in terms of the wall-normal coordinate [5]. Due to the no-slip condition, the zeroth-order terms in these expansions have to vanish. By incompressibility, the first-order term in the expansion of the wall-normal velocity component then also has to vanish. The tangential velocity components will, thus, be first order in the wall-normal coordinate, while the wall-normal velocity component exhibits a second-order near-wall scaling. The expansion of the velocity field can be inserted in subgrid-scale models (or other physical quantities based on the velocity field) to study their behavior near a solid wall.

Module

The nearWallScaling module of lesTools facilitates the study of the near-wall scaling behavior of physical quantities that are based on the velocity field of incompressible turbulent flows. This module can, for example, be used to analyze the near-wall scaling behavior of subgrid-scale models [6, 7].

Usage

Usage of the MATLAB scripts of the nearWallScaling module is explained in detail in the readme in the nearWallScaling folder of this toolbox.

Depending on your purposes, please consider citing the work by Silvis et al. [6] and/or Silvis and Verstappen [7] when making use of the nearWallScaling module.

References

  1. Sagaut, P. (2006). Large Eddy Simulation for Incompressible Flows: An Introduction. 3rd edn. Springer-Verlag Berlin Heidelberg. DOI: 10.1007/b137536.

  2. Pope, S. B. (2011). Turbulent Flows. Cambridge University Press.

  3. Nicoud, F., Ducros, F. (1999). “Subgrid-scale stress modelling based on the square of the velocity gradient tensor”. Flow, Turbulence and Combustion 62, pp. 183–200. DOI: 10.1023/A:1009995426001.

  4. Nicoud, F., Baya Toda, H., Cabrit, O., Bose, S., Lee, J. (2011). “Using singular values to build a subgrid-scale model for large eddy simulations”. Physics of Fluids 23, 085106. DOI: 10.1063/1.3623274.

  5. Trias, F. X., Folch, D., Gorobets, A., Oliva, A. (2015). “Building proper invariants for eddy-viscosity subgrid-scale models”. Physics of Fluids 27, 065103. DOI: 10.1063/1.4921817.

  6. Silvis, M. H., Remmerswaal, R. A., Verstappen, R. (2017). “Physical consistency of subgrid-scale models for large-eddy simulation of incompressible turbulent flows”. Physics of Fluids 29, 015105. DOI: 10.1063/1.4974093. PDF Abstract BibTeX BibLaTeX Cited by 32

  7. Silvis, M. H., Verstappen, R. (n.d.). “Creating physics-based subgrid-scale models for large-eddy simulation”. (in preparation).

  8. Silvis, M. H., Bae, H. J., Trias, F. X., Abkar, M., Verstappen, R. (2019). “A nonlinear subgrid-scale model for large-eddy simulations of rotating turbulent flows”. arXiv: 1904.12748 [physics.flu-dyn]. PDF Abstract BibTeX BibLaTeX Cited by 1

  9. Chapman, D. R., Kuhn, G. D. (1986). “The limiting behaviour of turbulence near a wall”. Journal of Fluid Mechanics 170, pp. 265–292. DOI: 10.1017/S0022112086000885.