The present work analyzes the quality and reliability of an important class of general-purpose, second-order accurate finite-volume (FV) solvers for the large-eddy simulation of a neutrally stratified atmospheric boundary layer (ABL) flow.
The analysis is carried out within the OpenFOAM^{®} framework, which is based on a colocated grid arrangement.
A series of open-channel flow simulations are carried out using a static Smagorinsky model for subgrid scale momentum fluxes in combination with an algebraic equilibrium wall-layer model.
The sensitivity of the solution to variations in numerical parameters such as grid resolution (up to

An accurate prediction of atmospheric boundary layer (ABL) flows is of paramount importance across a wide range of fields and applications, including weather forecasting, complex terrain meteorology, agriculture, air quality modeling, and wind energy

Since the early work of

The majority of the past work has relied on fully or partially dealiased mixed pseudospectral–finite-difference (PSFD) solvers – the go-to approach for LES studies since the works of

There is hence a growing interest from the ABL community in LES solvers based on compact spatial schemes via structured or unstructured meshes

Motivated by the aforementioned needs, the present study aims at characterizing the quality and reliability of an important class of second-order accurate FV solvers for the LES of neutrally stratified ABL flows.
The analysis is conducted in the open-channel flow setup (no Coriolis acceleration) via the OpenFOAM^{®} framework

The work is organized as follows. Section

We use index notation in a Cartesian reference system.
The spatially filtered Navier–Stokes equations are considered,

The large scale separation between near-surface and outer-layer energy-containing ABL motions poses stringent resolution requirements to numerical modelers, if all the energy containing motions have to be resolved.
To reduce the computational cost of such simulations, the near-surface region is typically bypassed and a phenomenological wall-layer model is leveraged instead to account for the impact of near-wall (inner-layer) dynamics on the outer-layer flow

In the present work,
the computational grid is colocated,
being the only colocated grid arrangement available within the OpenFOAM^{®} framework.
Note that
although advantageous in complex domains when compared to staggered grids ^{®} offers the standard Rhie–Chow correction

A series of WMLES of ABL flow (open-channel flow setup) is performed.
Tests are carried out in the domain

The computational mesh is Cartesian, with a uniform stencil along each direction.
Three simulations are run over

Tabulated list of cases.

This section is devoted to the analysis of velocity central moments (Sect.

Vertical structure of mean streamwise velocity

Figure

The vertical structure of turbulence intensities is also shown in Fig.

Relative error on the turbulence intensities

Skewness and kurtosis of the streamwise velocity (

Vertical structure of skewness of streamwise velocity

Relative error on skewness

One-dimensional spectra of streamwise velocity fluctuations (

Contours of two-dimensional spatial autocorrelation of streamwise velocity at height

To gain better insight on the spatial coherence of the flow field, the contour lines of the two-dimensional autocorrelation of the streamwise velocity

One-dimensional spatial autocorrelation of streamwise velocity at height

The one-dimensional spatial autocorrelation (

Integral lengths at height

Instantaneous snapshots of normalized streamwise velocity fluctuations at

Instantaneous snapshots of streamwise velocity fluctuations over a horizontal plane support the above findings (see Fig.

This section is devoted to the analysis of momentum transfer mechanisms in the ABL with a focus on quadrant analysis

The quadrant hole analysis is a technique based on the decomposition of the velocity fluctuations into four quadrants: the first and third quadrants,

Stress fractions at

Figure

Vertical structure of event ratios:

To gain insight on the vertical structure of momentum transfer mechanisms,
the exuberance ratio and the ratio of sweeps to ejections are analyzed in the following.
Figure

Visualization of the conditionally averaged velocity field in the cross-stream vertical plane at

Conditionally averaged flow field
from simulations FV

To conclude the analysis on the mechanisms responsible for momentum transfer, velocity statistics from a conditionally averaged flow field are discussed next.
The approach of

The present work provides insight on the quality and reliability of an important class of general-purpose, second-order accurate FV-based solvers for the wall-modeled LES of neutrally stratified ABL flow.
The considered FV-based solvers are part of the OpenFOAM^{®} framework, make use of the divergence form for the nonlinear term, and are based on a colocated grid arrangement.

A suite of simulations was carried out in an open-channel flow setup, varying the grid resolution up to

With the exception of the FV solver with the projection method and the Runge–Kutta time-advancement scheme, mean velocity profiles from the PSFD and FV solvers all feature a positive LLM. Existing techniques to alleviate this limitation led to no apparent improvement, thus calling for alternative approaches.

Near-surface streamwise velocity fluctuations are consistently overpredicted by both the PSFD and FV solvers, irrespective of the grid resolution. The overshoot is particularly pronounced for the cases based on the QUICK interpolation scheme. This behavior can be related to a deficit of pressure redistribution in the budget equations for the velocity variances, which results in a pile-up of shear-generated streamwise velocity fluctuations and deficit in the vertical and cross-stream velocity fluctuation components.

The interpolation scheme used for the discretization of the nonlinear term plays a role in determining the remaining flow statistics.
Specifically, FV solvers with a linear interpolation scheme lead to

a positive streamwise velocity skewness throughout the surface layer, which is at odds with experimental findings;

a severe overprediction of the streamwise velocity kurtosis;

a poorly correlated streamwise velocity field in the horizontal directions, especially at high grid resolutions;

a severe underprediction of outward and inward interactions and ejection events;

a lack of organized high- and low-momentum streaks and associated roll modes in the conditionally averaged flow field.

an improved prediction of the streamwise velocity skewness and kurtosis, especially as the grid stencil is reduced;

a streamwise velocity field that is more correlated along the horizontal directions, but integral length scales remain only a fraction of those from the PSFD and reference DNS results;

an underprediction of inward and outward interactions;

a lack of organized high- and low-momentum streaks and associated roll modes in the conditionally averaged flow field.

We here test the sensitivity of selected flow statistics to variations in the Smagorinsky constant ^{®}) are considered, and all tests are carried out at

As shown in Fig.

The one-dimensional spectra (Fig.

The performance of an alternative solver within the OpenFOAM^{®} framework is considered here, and the results are contrasted against those previously shown (obtained with the PISO algorithm in combination with an Adams–Moulton time-advancement scheme).
The solver is based on a projection method coupled with the Runge–Kutta 4 time-advancement scheme

The vertical profile of the mean streamwise velocity is shown in Fig.

Vertical structure of streamwise velocity

Normalized one-dimensional spectra of streamwise velocity at

Vertical structure of streamwise velocity

OpenFOAM^{®} is an open-source computational fluid dynamics toolbox.
The present study made use of OpenFOAM^{®} version 6.0, available for download at

Data and script to generate all figures in this manuscript can be downloaded from:

BG and MGG designed the study. BG conducted the analysis under the supervision of MGG. BG and MGG wrote the manuscript.

The authors declare that they have no conflict of interest.

The authors acknowledge computing resources from Columbia University's Shared Research Computing Facility project, which is supported by NIH Research Facility Improvement Grant 1G20RR030893-01, and associated funds from the New York State Empire State Development, Division of Science Technology and Innovation (NYSTAR) Contract C090171, both awarded 15 April 2010. The authors are grateful to Weiyi Li for generating the PSFD data, and to Ville Vuorinen and George I. Park for useful discussions on the performance of FV-based solvers for the simulation of turbulent flows.

The work was supported via start-up funds provided by the Department of Civil Engineering and Engineering Mechanics at Columbia University.

This paper was edited by Chiel van Heerwaarden and reviewed by two anonymous referees.

^{®}solver, Adv. Eng. Softw., 79, 70–80, 2015.