The worldwide expansion of wind energy is making the choice of potential wind farm locations more and more difficult. This results in an increased number of wind farms being located in complex terrain, which is characterised by flow separation, turbulence and high shear. Accurate modelling of these flow features is key for wind resource assessment in the planning phase, as the exact positioning of the wind turbines has a large effect on their energy production and lifetime. Wind modelling for wind resource assessments is usually carried out with the linear model Wind Atlas Analysis and Application Program (WAsP), unless the terrain is complex, in which case Reynolds-averaged Navier–Stokes (RANS) solvers such as WindSim and Ansys Fluent are usually applied. Recent research has shown the potential advantages of large-eddy simulation (LES) for modelling the atmospheric boundary layer and thermal effects; however, LES is far too computationally expensive to be applied outside the research environment. Another promising approach is the lattice Boltzmann method (LBM), a computational fluid technique based on the Boltzmann transport equation. It is generally used to study complex phenomena such as turbulence, because it describes motion at the mesoscopic level in contrast to the macroscopic level of conventional computational fluid dynamics (CFD) approaches, which solve the Navier–Stokes (N–S) equations. Other advantages of the LBM include its efficiency; near-ideal scalability on high-performance computers (HPCs); and ability to easily automate the geometry, the mesh generation and the post-processing. However, the LBM has been applied very little to wind modelling in complex terrain for wind energy applications, mainly due to the lack of availability of easy-to-use tools as well as the lack of experience with this technique. In this paper, the capabilities of the LBM to model wind flow around complex terrain are investigated using the Palabos framework and data from a measurement campaign from the Bolund Hill experiment in Denmark. Detached-eddy simulation (DES) and LES in Ansys Fluent are used as a numerical comparison. The results show that there is in general a good agreement between simulation and experimental data, and the LBM performs better than RANS and DES. Some deviations can be observed near the ground, close to the top of the cliff and on the lee side of the hill. The computational costs of the three techniques are compared, and it has been shown that the LBM can perform up to 5 times faster than DES, even though the set-up was not optimised in this initial study. It can be summarised that the LBM has a very high potential for modelling wind flow over complex terrain accurately and at relatively low costs, compared to solving N–S equations conventionally. Further studies on other sites are ongoing.

In order to assess the wind resource for both the planning and the assessment of wind farms, measurements and simulations of the prevailing wind conditions are required. Simulations are especially crucial in the observation of flows over complex terrain due to the large impact of steep inclines on the flow conditions. If the terrain shows only weak topographic changes or low hills, linear models can be used to make fast and sufficiently accurate yield forecasts

The detached-eddy-simulation (DES) method is a combination of LES and RANS. With this method, the flow is mostly calculated by LES, but the flow and vortices in wall regions are modelled by RANS. This method promises a strong reduction in the computational effort and the mesh requirements compared to LES. In addition, boundary layer modelling using RANS models makes it possible to use surface roughness models

An alternative to solving the N–S equations with great potential is the lattice Boltzmann method (LBM). The LBM has become more and more popular in recent years and is being continuously developed further. The LBM has also been used successfully for initial studies in the field of wind energy. Most of these studies focus on the simulation of flows around wind turbines and wind farms or analyse the wake behaviour of turbines (e.g.

The goal of this present paper is therefore to evaluate the capabilities of the LBM for wind modelling in complex terrain. Ansys Fluent is used as a reference for comparisons, using both a RANS and a DES approach. The paper starts with a brief introduction of the theories behind the LBM and the conventional N–S-based CFD calculations in Sect.

Interest in the LBM has been growing in the past decades as an efficient method for computing various fluid flows, ranging from low-Reynolds-number flows to highly turbulent flows (e.g.

The LBM has the following advantages over N–S: (1) it is a linear equation with only local non-linearity, making it more stable and perfectly scalable; (2) the dissipation is introduced locally by the collision term and does not depend on the lattice; and (3) the relaxation time includes both the regular viscous effects and its higher-order modifications. A description of the LBM can be found, for example in

a collision step where the BGK model is applied,

a streaming step,

Turbulence leads to the appearance of eddies with a wide range of length scales and timescales, which interact with each other in a dynamically complex way. Given the importance of the avoidance or promotion of turbulence in engineering applications, it is no surprise that a substantial amount of research effort is dedicated to the development of numerical methods to capture the important effects due to turbulence. The methods can be grouped into the following four categories:

turbulence models for Reynolds-averaged Navier–Stokes (RANS) equations,

large-eddy simulation (LES),

detached-eddy simulation (DES),

direct numerical simulation (DNS).

In this work, LES was applied for the LBM simulations. LES is an intermediate form of turbulence calculation which simulates the behaviour of the larger eddies. The method involves spacial filtering, which passes the larger eddies and rejects the smaller eddies. The effects on the resolved flow (mean flow plus large eddies) due to the smallest, unresolved eddies are included by means of a so-called sub-grid-scale model. It is assumed that the sub-grid scales have the effect of a viscosity correction, which is proportional to the norm of the strain-rate tensor at the level of the filtered scales:

The Bolund field campaign took place from December 2008 to February 2009 on Bolund Hill in Denmark. Bolund Hill is a 130 m long (east–west axis), 75 m wide (north–south axis) and 11.7 m high hill, situated near the Risø Campus of the Technical University of Denmark. Details of the experiment are described in

A contour map of Bolund Hill with meteorological masts denoted from M0 to M9

The LBM flow solver used in this work was the Palabos open-source library

To calculate the wind fields with Palabos in this work a 525 m long (east–west axis), 250 m wide (north–south axis) and 40 m high domain with a uniform grid resolution of

There are no turbulence closure models or surface roughness models implemented in the Palabos library yet; therefore the water surfaces were prescribed as free-slip bounce-back nodes and the ground surfaces were modelled using regularised bounce-back nodes

The inlet profile was described according to the Bolund Hill blind test specification for the westerly wind case. The logarithmic velocity profile is defined as

Ansys Fluent contains the broad, physical-modelling capabilities needed to model flow, turbulence, heat transfer and reactions for industrial applications, ranging from airflow over an aircraft wing to combustion in a furnace, from bubble columns to oil platforms, from blood flow to semiconductor manufacturing and from clean room design to wastewater treatment plants. For the Fluent simulations in this work the mesh was created with the new improved Fluent meshing tool; additionally the domain was extended to 830 m

The calculated velocity magnitude fields at a vertical plane through the position of met mast M3 for each measurement technique are shown in Figs.

Velocity field over the hill along the B line (LBM results):

Velocity field over the hill along the B line (Fluent results):

For a quantitative comparison, the same methodology is used as described by

As shown in Table

Speed-up along Bolund Hill. Wind direction is from 270

Turning along Bolund Hill. Wind direction is from 270

Turbulence kinetic energy (TKE) along Bolund Hill. Wind direction is from 270

Average speed-up error.

For the turning of the wind, a similar behaviour can be observed. The results match the experimental data very well at 5 m a.g.l., with all deviations lower than 3.0 % and the average turning error for each simulation technique shown in Table

Scatter plot of wind speeds, measurement against simulation results.

Average turning error.

Further analysis using the entire set of measurement data is shown in Fig.

Ratio of simulation results to experimental wind speeds as a function of elevation. The dotted grey line represents the average value.

Ratio of simulation results to experimental wind speeds as a function of measurement location. The dotted grey line represents the average value.

Finally Fig.

Comparison of computational time per CPU core and million cells.

In this section, the performance of the simulation techniques is compared in terms of the computational costs. This has been done because the overall cost of a simulation is an important factor for modellers, who need to choose the most suitable model for a given wind energy project. The results of this work have been used in order to develop a new method for helping wind modellers choose the most cost-effective model for a given project. This was done by first defining various parameters for predicting the skill and cost scores before carrying out the simulations as well as for calculating skill and cost scores after carrying out the simulations. Weightings were then defined for these parameters, and values assigned to them for a range of tools, including the ones applied in the present work, using a template containing predefined limits in a blind test. This allowed for a graph of predicted skill score against cost score to be produced, enabling modellers to choose the most cost-effective model without having to carry out the simulations beforehand. More details can be found in

Figure

Computational time. All simulation were run on 80 cores (Intel Xeon E5-2630v4 2.2 GHz).

In this study, LES using the LBM framework Palabos was implemented to calculate the wind field over the complex terrain of Bolund Hill. Advantages of the LBM include its efficiency; near-ideal scalability on high-performance computers (HPCs); and capabilities to easily automate the geometry, the mesh generation and the post-processing.

The results were compared to RANS simulations and DESs using Ansys Fluent and field measurements. In general there was a good agreement between simulation and experimental data. The average wind speed-up error compared to measurements was 8.0 % for the LBM, 17.3 % for DES and 10.0 % for RANS. The average wind turning error compared to measurements was 2.7

The computational costs of these three models were compared, and it has been shown that the LBM, even in this set-up of the simulation which has not yet been fully optimised, can perform 5 times faster than DES and lead to slightly more accurate results.

It can be summarised that the LBM may be applicable to modelling wind flow over complex terrain accurately at relatively low costs if the challenges raised in this work are addressed. Further studies on other sites are ongoing.

The non-dimensioning procedure used in this study is carried out according to the similarity theory. It consists of two steps. First a physical system is converted into a dimensionless system, independent of the original physical scales but also independent of simulation parameters. In a second step, the dimensionless system is converted into a discrete simulation. Thus the dimensionless level (

The simulation set-up repository is available via

The contribution of the authors in this paper was as follows:

AS carried out and analysed the simulations.

SB managed the project and corrected the paper.

HN supervised AS and corrected the paper.

The authors declare that they have no conflict of interest.

This article is part of the special issue “Wind Energy Science Conference 2019”. It is a result of the Wind Energy Science Conference 2019, Cork, Ireland, 17–20 June 2019.

Thanks go to the funder of this project: the Swiss Federal Office of Energy.

This paper was edited by Johan Meyers and reviewed by two anonymous referees.