the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 18 Aug 2025
Enabling the use of unstructured meshes for the Large Eddy Simulation of stable atmospheric boundary layers
Abstract. Modelling wind flows over complex terrain under varying atmospheric stability conditions is essential for improving our understanding of atmospheric boundary layer physics and its impact on wind energy systems. However, such simulations remain challenging due to the limitations of structured grids in representing complex geometries and the inherent difficulty of modelling the stable boundary layer, characterized by small-scale turbulent structures. These challenges necessitate the use of high-fidelity simulations with unstructured meshes, which offer greater geometric flexibility. Nevertheless, unstructured grids are rarely used in atmospheric simulations. This study establishes a baseline framework for the use of unstructured meshes in atmospheric boundary layer simulations, with particular relevance to complex terrain. The proposed solver is validated against two well-established benchmarks under neutral and stable stratification. For the neutral case, the Andrén benchmark, a 1.28 × 1.28 × 1.5 km3 periodic domain where the flow is driven by a large-scale pressure gradient, is considered. Results from structured and unstructured grids are in good agreement, with minor differences observed near the surface. Unstructured grids exhibit slightly higher friction velocities due to wall-proximal grid quality, but remain within the expected variability of existing studies. The solver is then applied to the GABLS1 stable boundary layer case, a 400 × 400 × 400 m3 domain with surface cooling. Both grid types capture the evolution of the SBL, with unstructured grids yielding higher surface heat fluxes – up to 14 % – resulting in a thicker boundary layer and noticeable differences in mean profiles and fluxes. A mesh refinement study confirms that a horizontal resolution of ∆x = 6.25 m is sufficient for accurate SBL representation with both mesh types. Overall, the results demonstrate that unstructured meshes are a viable and robust tool for atmospheric boundary layer modelling, capable of matching the accuracy of structured grids while offering the flexibility required for complex terrain. The minor discrepancies observed remain within the variability expected from model formulation choices. This work thus provides a foundational reference for future high-fidelity atmospheric simulations using unstructured grids, particularly in terrain-resolving contexts.
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Status: final response (author comments only)
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RC1: 'Comment on wes-2025-141', Anonymous Referee #1, 12 Sep 2025
- AC1: 'Reply on RC1', ulysse vigny, 11 Nov 2025
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RC2: 'Comment on wes-2025-141', Anonymous Referee #2, 03 Oct 2025
Review of the manuscript “Enabling the use of unstructured meshes for the Large Eddy Simulation of stable atmospheric boundary layers” by Ulysse Vigny, Léa Voivenel, Mostafa Safdari Shadloo, Pierre Bénard, and Stéphanie Zeoli submitted for publication in Wind Energy Science.
In the manuscript “Enabling the use of unstructured meshes for the Large Eddy Simulation of stable atmospheric boundary layers” the authors present validation of an unstructured large-eddy simulation model for simulation of atmospheric boundary layer flows.
General Remarks
In the manuscript the validation of an unstructured LES code is presented in clear and logical way. The validation of an unstrucured grid model can be of interest for the wind energy community. However, the selected test cases are very basic horizontally homogeneous atmospheric boundary layers (ABLs): a neutrally stratified atmospheric boundary layer case based on Andren (1994) paper, and a stably stratified case based on GABLES 1 intercomparison study (Beare et al., 2006). While these cases demonstrate the ability of the model to generally reproduce the structure of these ABLs, they do not demonstrate the advantage of using unstructured grids. Unstructured grids could be advantageous for simulation of flows in complex terrain or around structures (e.g., urban flow simulations). However, structured grids have been successfully used for such simulations when combined with immersed boundary or immersed force approaches (e.g., Lundquist et al. 2009, MWR; Arthur et al. 2018, MWR; Muñoz-Esparza et al. 2020, JAMES). When also combined with mesh refinement, structured grid models can be used to resolve structures in high detail (e.g., Energy Research and Forecasting model, https://github.com/erf-model/ERF; Lattanzi et al. 2024, arXiv, to appear in JAMES). The authors do not address this possibility and contrast unstructured grids with structured grids including immersed boundary approach and mesh refinement.
In the neutrally stratified case, the unstructured model produces higher velocity variances, while in stably stratified case it also results in higher turbulent stresses. The authors attribute this to “increased resolved turbulence, which can be attributed to differences in near-wall resolution and numerical dissipation.” This argument is not convincing; a reason for differences in near-wall resolution should be provided, also, it is not clear why would numerical dissipation be lower for the unstructured grid with the same number of degrees of freedom and the same numerical scheme as on the structured grid. What is missing is the spectral analysis to demonstrate that unstructured grid can accurately reproduce energy cascade and that the enhanced variances are not result of inaccuracies in the energy cascade from large to small scales. While spectral analysis of unstructured grids is not straight forward – it can be accomplished either by interpolation (e.g., Juricke et al. 2022, JAMES) or by analyzing time series at a point (or better many points in space). The differences between results obtained using the structured and the unstructured grid should not be attributed to supposedly lower numerical dissipation without evidence. Furthermore, it would be important to provide comparison of computational performance of the unstructured and structured models for the same number of degrees of freedom.
Taking all the above into consideration I think that the manuscript can be published in the journal Wind Energy Science after the authors address comments outlined above and Specific Remarks listed below.
Specific Remarks
Equation 1 – Since the model is incompressible and Boussinesq approximation is used it would be important to include the equation for the potential temperature and replace density with potential temperature.
Line 91 – It should be “Absolute value of the Obukhov lengths,” since in unstably stratified case the length scale is negative.
Subsection 2.3 – Number of degrees of freedom (nodes) should be given for both, structured and unstructured grids.
Line 129 – Since the model is incompressible, constant (and uniform) density, it is not clear what is meant by “reference density.” It should be a reference temperature.
Line 150 – Elevated values of the friction velocity in case of the unstructured grid are attributed to increased numerical diffusion, however, later the elevated levels of velocity variances in simulations with the unstructured grid are attributed to lower numerical dissipation. These two statements cannot be easily reconciled. It is not obvious if they both can hold simultaneously. The authors should provide clear explanation.
Figure 3 – Shown is only resolves turbulent stress since it is zero at the surface. It would be important to plot total turbulent stress, resolved and subgrid as it is commonly done (e.g., Figure 7 a) in Chow et al. 2005, JAS, cited in the manuscript).
Figure 8 – Same as for Figure 3.
Figure 14 – Same as for Figure 3.
Citation: https://doi.org/10.5194/wes-2025-141-RC2 - AC2: 'Reply on RC2', ulysse vigny, 11 Nov 2025
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