Numerical enhancement of a mesoscale model for large-eddy simulation of the wind over steep terrain

Mesoscale modelling of the atmospheric boundary layer has advanced significantly over the past decades, although there are still different numerical aspects that must be enhanced to achieve accurate wind simulations over steep topography. This has become a necessity since many applications, such as wind resource assessment, now require high fidelity results for viability analysis and decision-making. With the advent of high performance computing and more sophisticated software, the wind energy industry is increasingly interested in multiscale models based on combined configurations capable of yielding higher resolution results. The size of the modern wind farms now requires a multiscale analysis that allows the evaluation of the joint meso- and microscale processes triggered over complex topography. For this reason, mesoscale models with imbedded large-eddy simulation capabilities are well suited to become the next mainstream family of simulation toolkits for wind engineering. The Mesoscale Compressible Community (MC2) model, subject of this work, is a good example since it is employed as the kernel of the Wind Energy Simulation Toolkit (WEST), introduced by the Recherche en Prévision Numérique (RPN) group of Environment Canada. MC2 performs well for wind simulations over flat, gentle and moderate terrain slopes, which led the wind energy community to be confident enough on employing it to generate the Canadian Wind Atlas. However, as with other similar models, several numerical issues such as wind overestimation and distorted circulation patterns have been identified in recent years from orographic flow simulations in presence of steep slopes. Hence, wind resource assessment over high impact topography, such as the Rocky Mountains or the Niagara Escarpment, cannot be entirely reliable and needs a revaluation with enhanced multiscale modelling. By applying an eigenmode analysis, we have recognized the numerical instability and precisely measured the spurious noise problem, inherent of MC2’s classical three time-level semi-implicit (SI) scheme. With the appropriate redefinition of the prognostic thermodynamic variables, the SI time discretization, coupled with the semi-Lagrangian (SL) scheme, is now consistently structured in a way that it enables MC2 to solve the compressible non-hydrostatic Euler equations (EE) in a more stable and accurate fashion. MC2 is now able to perform wind simulations over steep slopes in the absence of time decentering, frequency filtering and other numerical damping mechanisms. Additionally, the climate-state classification of the statistical-dynamical downscaling (SDD) method is upgraded by including the Brunt-Väisälä frequency that accounts for the atmospheric thermal stratification effect on wind flow over topography. The present study provides a real orographic flow validation of these numerical enhancements in MC2, assessing their individual and combined contribution for an improved initialization and calculation of the surface wind in presence of high-impact terrain. Lastly, the metric tensor adaptation of MC2’s imbedded large-eddy simulation (LES) method, necessary for wind modelling over mountainous terrain, has been achieved preserving the enhanced numerical stability and accuracy. Test results indicate that the enhanced MC2-LES model reproduces efficiently the expected flow patterns, separation and recirculation zone over steep terrain, and yields accurate results comparable to those reported from experimental data or by other researchers who use numerical models with similar or more sophisticated turbulence closure schemes

A nonhydrostatic unstructured-mesh soundproof model for simulation of internal gravity waves

A semi-implicit edge-based unstructured-mesh model is developed that integrates nonhydrostatic soundproof equations, inclusive of anelastic and pseudo-incompressible systems of partial differential equations. The model builds on nonoscillatory forward-in-time MPDATA approach using finite-volume discretization and unstructured meshes with arbitrarily shaped cells. Implicit treatment of gravity waves benefits both accuracy and stability of the model. The unstructured-mesh solutions are compared to equivalent structured-grid results for intricate, multiscale internal-wave phenomenon of a non-Boussinesq amplification and breaking of deep stratospheric gravity waves. The departures of the anelastic and pseudo-incompressible results are quantified in reference to a recent asymptotic theory [Achatz et al. 2010, J. Fluid Mech., 663, 120-147)]

Non-oscillatory forward-in-time integrators for viscous incompressible flows past a sphere

A non-oscillatory forward-in-time (NFT) integrator is developed to provide solutions of the Navier-Stokes equations for incompressible flows. Simulations of flows past a sphere are chosen as a benchmark representative of a class of engineering flows past obstacles. The methodology is further extended to moderate Reynolds number, stably stratified flows under gravity, for Froude numbers that typify the characteristic regimes of natural flows past distinct isolated features of topography in weather and climate models. The key elements of the proposed method consist of the Multidimensional Positive Definite Advection Transport Algorithm (MPDATA) and a robust non-symmetric Krylov-subspace elliptic solver. The solutions employ a finite volume spatial discretisation on unstructured and hybrid meshes and benefit from a collocated arrangement of all flow variables while being inherently stable. The development includes the implementation of viscous terms with the detachededdy simulation (DES) approach employed for turbulent flows. Results demonstrate that the proposed methodology enables direct comparisons of the numerical solutions with corresponding laboratory studies of viscous and stratified flows while illustrating accuracy, robustness and flexibility of the NFT schemes. The presented simulations also offer a better insight into stably stratified flows past a sphere

DCMIP2016: a review of non-hydrostatic dynamical core design and intercomparison of participating models

Atmospheric dynamical cores are a fundamental component of global atmospheric modeling systems and are responsible for capturing the dynamical behavior of the Earth's atmosphere via numerical integration of the Navier-Stokes equations. These systems have existed in one form or another for over half of a century, with the earliest discretizations having now evolved into a complex ecosystem of algorithms and computational strategies. In essence, no two dynamical cores are alike, and their individual successes suggest that no perfect model exists. To better understand modern dynamical cores, this paper aims to provide a comprehensive review of 11 non-hydrostatic dynamical cores, drawn from modeling centers and groups that participated in the 2016 Dynamical Core Model Intercomparison Project (DCMIP) workshop and summer school. This review includes a choice of model grid, variable placement, vertical coordinate, prognostic equations, temporal discretization, and the diffusion, stabilization, filters, and fixers employed by each syste

3D cut-cell modelling for high-resolution atmospheric simulations

Owing to the recent, rapid development of computer technology, the resolution of atmospheric numerical models has increased substantially. With the use of next-generation supercomputers, atmospheric simulations using horizontal grid intervals of O(100) m or less will gain popularity. At such high resolution more of the steep gradients in mountainous terrain will be resolved, which may result in large truncation errors in those models using terrain-following coordinates. In this study, a new 3D Cartesian coordinate non-hydrostatic atmospheric model is developed. A cut-cell representation of topography based on finite-volume discretization is combined with a cell-merging approach, in which small cut-cells are merged with neighboring cells either vertically or horizontally. In addition, a block-structured mesh-refinement technique is introduced to achieve a variable resolution on the model grid with the finest resolution occurring close to the terrain surface. The model successfully reproduces a flow over a 3D bell-shaped hill that shows a good agreement with the flow predicted by the linear theory. The ability of the model to simulate flows over steep terrain is demonstrated using a hemisphere-shaped hill where the maximum slope angle is resolved at 71 degrees. The advantage of a locally refined grid around a 3D hill, with cut-cells at the terrain surface, is also demonstrated using the hemisphere-shaped hill. The model reproduces smooth mountain waves propagating over varying grid resolution without introducing large errors associated with the change of mesh resolution. At the same time, the model shows a good scalability on a locally refined grid with the use of OpenMP.Comment: 19 pages, 16 figures. Revised version, accepted for publication in QJRM

Combination of WENO and Explicit Runge–Kutta Methods for Wind Transport in the Meso-NH Model

This paper investigates the use of the weighted essentially nonoscillatory (WENO) space discretization methods of third and fifth order for momentum transport in the Meso-NH meteorological model, and their association with explicit Runge–Kutta (ERK) methods, with the specific purpose of finding an optimal combination in terms of wall-clock time to solution. A linear stability analysis using von Neumann theory is first conducted that considers six different ERK time integration methods. A new graphical representation of linear stability is proposed, which allows a first discrimination between the ERK methods. The theoretical analysis is then completed by tests on numerical problems of increasing complexity (linear advection of high wind gradient, orographic waves, density current, large eddy simulation of fog, and windstorm simulation), using a fourth-order-centered scheme as a reference basis. The five-stage third-order and fourth-order ERK combinations appear as the time integration methods of choice for coupling with WENO schemes in terms of stability. An explicit time-splitting method added to the ERK temporal scheme for WENO improves the stability properties slightly more. When the spatial discretizations are compared, WENO schemes present the main advantage of maintaining stable, nonoscillatory transitions with sharp discontinuities, but WENO third order is excessively damping, while WENO fifth order provides better accuracy. Finally, WENO fifth order combined with the ERK method makes the whole physics of the model 3 times faster compared to the classical fourth-order centered scheme associated with the leapfrog temporal scheme

Development of a canopy stress method for large eddy simulation over complex terrain

High-fidelity Large-Eddy Simulation (LES) of fluid flow over complex terrain has long been a challenging computational problem. Complex terrain leads to increased velocity gradients, turbulence production, and complex turbulent wakes. Body-fitted grids need a high resolution to deal with additional effects of highly skewed cells that follow a terrain of steep slope. Immersed boundary methods need special techniques like wall models to numerically resolve the associated drag force. In flow over complex terrain, the characteristic scale decreases locally which makes it a challenging endeavour for LES to mimic the turbulent energy cascade, particularly when steep terrain produce vortices and streaky structures that sustain turbulence away from the surface. This thesis presents the canopy stress method in which the terrain is immersed into the fluid, cutting the cells of a Cartesian grid, where the effects of terrain are treated by the form drag and the skin friction drag. Heat transfer analysis of flow in pipes and porous media is considered to study the sensitivity of canopy drag coefficients. A scale-adaptive methodology is proposed to model the subgrid-scale terrain effects. The analysis of wind tunnel measurements over mountains and forests shows that the scale-adaptive model dynamically adjusts the dissipation rate by the scale of energetic eddies near complex terrain. In regions without terrain effects, where subgrid turbulence is locally isotropic, the model also provides accurate dissipation rate. These results suggest that combining the rotation tensor and the vortex stretching vector with the strain tensor through the second-invariant of the square of the velocity gradient tensor is a novel approach to improve the fidelity of LES over complex terrain in which the dissipation becomes scale-aware; i.e. the rate of turbulence dissipation is adjusted with the changes in the characteristic scales. The numerical analysis of four distinct flow regimes (e.g., Chapters 3-6) illustrates the accuracy, simplicity, and cost-effectiveness of the proposed LES methodology

Simulations of wind formation in idealised mountain–valley systems using OpenFOAM

An OpenFOAM computational fluid dynamics model setup is proposed for simulating thermally driven winds in mountain–valley systems. As a first step, the choice of Reynolds Averaged Navier–Stokes k-e turbulence model is validated on a 3D geometry by comparing its results vs. large-eddy simulations reported in the literature. Then, a numerical model of an idealised 2D mountain–valley system with mountain slope angle of 20° is developed to simulate thermally driven winds. A couple of top surface boundary conditions (BC) and various combinations of temperature initial conditions (IC) are tested. A transient solver for buoyant, turbulent flow of incompressible fluids is used. Contrary to classical approaches where buoyancy is set as a variable of the problem, here temperature linearly dependent with altitude is imposed as BC on the slope and successfully leads to thermally driven wind generation. The minimum fluid domain height needed to properly simulate the thermally driven winds and the effects of the different setups on the results are discussed. Slip wall BC on the top surface of the fluid domain and uniform temperature IC are found to be the most adequate choices. Finally, valleys with different widths are simulated to see how the mountain–valley geometry affects the flow behaviour, both for anabatic (daytime, up-slope) and katabatic (nighttime, down-slope) winds. The simulations correctly reproduce the acceleration and deceleration of the flow along the slope. Increasing the valley width does not significantly affect the magnitude of the thermally driven wind but does produce a displacement of the generated convective cell.This research was funded by AGAUR/Generalitat de Catalunya, with grant number 2017 SGR 1278, and by the Spanish Science and Innovation Ministry (MCIN) within the project TABL4CW, with grant number PID2019-105162RB-I00, funded by MCIN/AEI/10.13039/501100011033.Objectius de Desenvolupament Sostenible::7 - Energia Assequible i No ContaminantObjectius de Desenvolupament Sostenible::7 - Energia Assequible i No Contaminant::7.2 - Per a 2030, augmentar substancialment el percentatge d’energia renovable en el con­junt de fonts d’energiaPostprint (published version

Cut Cell Methods in Global Atmospheric Dynamics

In this thesis, we study next generation techniques for the numerical simulation of global atmospheric dynamics, which range from modeling and grid generation to discretization schemes. Based on a detailed dimensional analysis of the compressible three-dimensional Navier-Stokes equations for small- and large-scale motions in the atmosphere, we derive the compressible Euler equations, the dynamical core of meteorological models. We also provide an insight into multiscale modeling and present a new numerical way of deriving reduced atmospheric models and gaining consistency of the modeling and discretization errors. The main focus of this thesis is the grid generation of the atmosphere. With regard to newly available surveys of the Earth's surface and the ever increasing computing capacities, the atmospheric triangulation techniques have to be reconsidered. In particular, the widely-used terrain-following coordinates prove to be disadvantaguous for highly resolved grids, since both the pressure gradient force error and the hydrostatic inconsistency of this vertical ansatz seriously increase with finer resolution. After a detailed analysis of the standard methods for vertical atmospheric triangulations, we present the cut cell approach as capable alternative. We construct a special cut cell method with two stabilizing constraints and provide a comprehensive guideline for an implementation of cut cells into existing atmospheric codes. For the spatial discretization of the dynamical core, we choose the Finite Volume method because of its favorable characteristics concerning conservation properties and handling of hyperbolicity. We accompany the Finite Volume discretization by a new non-linear interpolation scheme of the velocity field, which is adapted to the geometry and rotation of the Earth. To fathom the capabilities of cut cell grids together with our discretization and new interpolation scheme, we finally present several three-dimensional simulation runs. We apply standard benchmarks like an advection test and the simulation of a Rossby-Haurwitz wave and construct a new test case of counterbalancing flow between high- and low-pressure areas, with which we expose the potential of cut cell methods and the influences of different effects of the Euler equations as well as the topography of the Earth

Response of the wind-turbine wake to a turbulent atmospheric boundary-layer flow

Die Eigenschaften des Nachlaufs einer Windturbine werden für verschiedene im Laufe eines Tages in einer turbulenten Grenzschicht auftretende atmosphärische Schichtungen mit Grobstruktursimulationen mit dem Strömungslöser EULAG untersucht. Dafür wurde eine Methode zur Erhaltung der Hintergrundturbulenz für Windturbinensimulationen mit offenen Randbedingungen in Strömungsrichtung entwickelt. Dies wird durch das Aufprägen der turbulenten Fluktuationen in der spektralen Energieverteilung einer neutralen Grenzschicht ermöglicht. Weiter lässt sich damit das permanente Einlesen von turbulenten Einströmprofilen in die Windturbinensimulationen vermeiden. Zusätzlich wurden idealisierte Tagesgangsimulationen über homogenen und heterogenen Oberflächen durchgeführt. Der Tagesgang zeigt einen signifikanten Einfluss auf den Wind und die Turbulenz in der atmosphärischen Grenzschicht. Unter homogenen Bedingungen treten in der stabilen und der morgendlichen Grenzschicht eine starke vertikale Windscherung und eine Änderung der Windrichtung mit der Höhe auf, wohingegen in der konvektiven und der abendlichen Grenzschicht die Turbulenz in der Atmosphäre stark ausgeprägt ist. Unter heterogenen Bedingungen hat die nächtliche Zunahme der Scherung einen grossen Einfluss auf Wind und Turbulenz, und führt zu einer Kompensation der Ekmanspirale. Windturbinensimulationen werden mit synchronisierten Daten aus den Tagesgangsimulationen betrieben. Die sich ergebenden Nachläufe sind von der Stabilität der Atmosphäre beeinflusst und haben ihrerseits einen Einfluss auf die Energieeffizienz der Windturbine. Das Strömungsfeld wird durch eine schnellere Einmischung unter konvektiven Bedingungen am Tag, im Gegensatz zur Nacht, geprägt. Die Nachläufe, die sich in der abendlichen und morgendlichen Grenzschicht entwickeln, sind entscheidend von der vorhergehenden atmosphärischen Situation beeinflusst. Um diese äusserst rechenintensiven Tagesgangsimulationen zu vermeiden, wurde die Methode zur Aufrechterhaltung der Hintergrundturbulenz zu einer Parametrisierung ausgeweitet. Diese beinhaltet eine schichtungsspezifische Gewichtung sowie entsprechende Hintergrundwindprofile, beides aus der idealisierten Tagesgangsimulation über homogener Oberfläche abgeleitet. Die Windturbinensimulationen mit Parametrisierung zeigen eine gute Übereinstimmung mit den synchronisierten Windturbinensimulationen aus der Tagesgangsimulation über homogener Oberfläche und reduzieren die erforderliche Rechenzeit um den Faktor 100. Dies spricht für eine einfache und äusserst effiziente Parametrisierung des turbulenten einströmenden Windfeldes für Grobstruktursimulationen unterschiedlicher thermischer Schichtungen.The wake characteristics of a wind turbine for different regimes occurring throughout the diurnal cycle are investigated systematically by means of large-eddy simulation with the geophysical flow solver EULAG. A methodology to maintain the turbulence of the background flow in wind-turbine simulations with open streamwise boundaries, without the necessity of the permanent import of turbulence data, was developed. These requirements are fulfilled by applying the turbulent fluctuations of the spectral energy distribution of a neutral boundary layer in the wind-turbine simulations. Further, idealized diurnal cycle simulations over homogeneous and heterogeneous surface were performed. Under homogeneous conditions, the diurnal cycle significantly impacts the low-level wind shear and the atmospheric turbulence. A strong vertical wind shear and veering with height occur in the nocturnal stable boundary layer and in the morning boundary layer, whereas the atmospheric turbulence is much larger in the convective boundary layer and in the evening boundary layer. The increased shear under heterogeneous conditions change these characteristics, counteracting the formation of the night-time Ekman spiral. Synchronized turbulent inflow data from the diurnal cycle simulations drive the wind-turbine simulations. The resulting wake is strongly influenced by the stability of the atmosphere and has an impact on the efficiency of the wind turbine. The flow in the wake recovers more rapidly under convective conditions during the day, than under stable conditions at night. The wake characteristics of the transitional periods are influenced by the flow regime prior to the transition. To alleviate the computational extremely expensive diurnal cycle simulations, the turbulence preserving method was extended to a parameterization, which includes a stratification related weighting and suitable background wind profiles, both resulting from the idealized diurnal cycle precursor simulation over homogeneous surface. The following parameterization wind-turbine simulations are in good agreement with the synchronized diurnal cycle wind-turbine simulations over homogeneous surface and reduce the computational costs by a factor of 100. Therefore, they result in a simple, numerically efficient, and computationally fast parameterization of turbulent wind-turbine flows for large-eddy simulations of different thermal stratifications