Smagorinsky Subgrid-scale Model Research Articles

Vector form of intrinsic finite element method for incompressible fluids

Vector form of intrinsic finite element (VFIFE) is a numerical method widely used in solid mechanics. However, it's hard to extend the VFIFE method to fluid mechanics since the traditional VFIFE method fails to reflect the analytical equilibrium of multiple variables in the continuum. Therefore, under the framework of analytical mechanics, this paper proposes Lagrange's equation of the second kind in fluid mechanics with the extremum condition of Lagrange power functional. And a vectorized motion equation of incompressible viscous fluids is deduced from Lagrange's equation. By using several efficient algorithms in the finite difference method (FDM) and the finite element method (FEM), the NS equation is decomposed into four governing equations of vector form for fluid mechanics. In addition, with the application of the classic Smagorinsky sub-grid scale model in large eddy simulation (LES), this paper puts forward turbulence modelling with VFIFE procedure, and a corresponding MATLAB program is developed. Two typical examples are given to demonstrate the applicability and efficiency of the proposed large eddy simulation with VFIFE method. The proposed algorithm can effectively eliminate the non-physical oscillation of the pressure, and obtain much accurate results with a small number of grids.

Large eddy simulation of a turbulent channel flow using dynamic Smagorinsky subgrid scale model and differential equation wall model

A large eddy simulation (LES) is conducted in a plane channel flow which is turbulent. For understanding the mechanism of the turbulent motion more efficiently, the present study is an attempt to conduct the LES using a Dynamic Smagorinsky Model (DSM) and a Differential Equation Wall Model (DEWM). DSM is a subgrid-scale model and DEWM is for approximating the near wall layer. The simulation is performed in a domain of 2 π δ × 2 δ × π δwhich is discretized by 32 × 20 × 32grid points where δ is the channel half width. The discretization techniques have been used in the simulation, are the 3rd order low storage R-K method in time and 2nd order finite difference formulation in space. To assess the performance of the LES with DSM and DEWM, the simulation results are compared with direct numerical simulation (DNS) data and LES data using Standard Smagorinsky Model (SSM). Comparing the results in the essential turbulence statistical field it has been found that DSM performs better than SSM in most of the cases and shows better agreement with the DNS results. Flow structures in the turbulent flow field are compared in isosurfaces and contour plots, and found that tube-like vortical structures are randomly distributed over the entire flow field, and the number of the vortical structures are more for the DSM case than that of SSM.

Wind Tunnel and Grid Resolution Effects in Large-Eddy Simulations of the High-Lift Common Research Model

This paper describes the application of a compressible large-eddy simulation (LES) solver to the flow over the High-Lift Common Research Model (CRM-HL) in landing configuration, a complex external aerodynamic flow configuration with deployed slats, flaps, a flow-through nacelle, and the associated brackets/fairings on the high-lift devices. The bulk Mach number is (0.2) and the mean-aerodynamic-chord-based Reynolds number is typical of a wind tunnel experiment (5.49E6). A key development in these simulations relative to previous work is that this work serves to establish robustness of LES methods to Reynolds number and aircraft configuration. Previous studies focused on the Japan Aerospace Exploration Agency Standard Model, which featured a nearly 3× lower Reynolds number than the present CRM-HL investigation and less aggressive wing/slat leading-edge curvature than the CRM-HL geometry, which led to lower leading-edge pressure suction peak magnitudes, both of which led to less stringent grid resolution requirements. In these LES simulations, an algebraic equilibrium wall modeling approach is employed along with a dynamic implementation of the Smagorinsky subgrid-scale model. The calculations are carried out in both a free air setting and one that includes the wind tunnel facility at seven angles of attack at five grid resolution levels, ranging from ≈10 to 1500 million control volumes. In free air, the solutions show decreasing sensitivity to the grid with each successive refinement level and systematically approach the experimental lift coefficient data as the grid is refined, with the 1.5 billion control volume case showing excellent agreement with the corrected experimental data. The simulations in both free air and in the wind tunnel predict a stall mechanism featuring a large inboard juncture stall and a nose-down break in the pitching moment curve, both of which agree with the experimental observations. The accuracy of the simulations is assessed via comparisons of integrated forces/moments, surface pressures, and surface skin friction visualizations. Graphics processing unit (GPU) acceleration of the charLES solver results in tractable turnaround times that make LES a useful tool in the aerospace industry design cycle. Recent GPU acceleration of the flow solver has made LES solutions that are highly accurate in lift/drag/moment for relevant high-lift aircraft flows achievable within about 5 h of wall time on 600 GPU cores.

Large-eddy simulation of airflow dynamics around a cluster of buildings

The wind flow around the buildings with different rooftops is studied numerically using large-eddy simulation (LES). The filtered Navier-Stokes equations in LES are used to compute the large eddies, whereas the dynamic Smagorinsky subgrid-scale (SGS) model calculates the small eddies. A turbulent spot method is applied for the synthesis of artificial turbulent fields at the inlet. In this separated and reattached flow, our aim is to analyze the wakes’ vortical structure along with the buildings of different heights and shapes. A large number of engineering applications involve precise predictions of the airflow around buildings to ensure performance and safety. To validate the numerical solver, a comparison is performed with the earlier reported numerical and experimental data. The turbulent flow characteristics are discussed in terms of instantaneous flow structure and time-averaged statistical flow quantities. All the cases are simulated for a Reynolds number [Formula: see text] to understand the turbulent airflow patterns. The flow shows a separable bubble at the leading edge of the rooftop of the building that leads to recirculation at the lee side of the first row of buildings. Due to the recirculation, the suction arises near the leading edge of the building to assure a continuous flow of air around the obstacles. Further, Reynold stresses show high momentum fluxes in the frontal region of the buildings.

The Impact of Increasing the Length of the Conical Segment on Cyclone Performance Using Large-Eddy Simulation

In cyclone separators, the asymmetrical coherent structure significantly influences the velocity fluctuations and hence the cyclone performance. This asymmetric rotating vortex in the core region precesses around the cyclone axis with a frequency that depends on the cyclone geometry and operating conditions. In the present work, we studied the impact of increasing the length of the conical segment on the performance of cyclone separators as well as the precessing frequency of the asymmetrical structure. For this, five different cone lengths were considered such that the total cyclone length equalled 3.0D, 3.5D, 4.0D, 4.5D, and 5.0D (here, D is the main body diameter of the cyclone). The study was performed at three different inlet velocities, viz. 10, 15, and 20 m/s. Throughout the work, the angle of the conical segment was held fixed and resembled the reference model (which had a total cyclone length equal to 4.0D). The cyclone performance was evaluated using advanced closure large-eddy simulation with the standard Smagorinsky subgrid-scale model. Conclusive results indicate that with an increase in the cone length, the pressure losses reduce appreciably with small variations in the collection efficiency, followed by a reduction in the precessing frequency of the asymmetric vortex core. The results further indicate that the apex cone angle (or the bottom opening diameter) must be carefully adjusted when increasing the cone length.

Assessment of a Differential Subgrid Stress Model for Large-Eddy Simulations of Turbulent Unconfined Swirling Flames

Swirling flames are widely used in engineering to intensify mixing and stabilize combustion in gas turbine power plants and industrial burners. Swirling induces new instability modes, leading to intensification of coherent structures, asymmetric geometry, vortex core precession, and flame oscillations. Large-Eddy Simulation (LES) has the capability to furnish more accurate and reliable results than the simulations based on Reynolds-averaged Navier–Stokes equations (RANS). Subgrid-scale models in LES need to describe the backscatter (local transfer of kinetic energy from small scales to larger scales) that is intensified in swirling flames. In this paper, the Differential Subgrid Stress Model (DSM), previously developed by the authors, is assessed using an experimental database from Sydney University on swirl-stabilized turbulent unconfined non-premixed methane-air flame. Regime without vortex precession is simulated numerically using the DSM and Smagorinsky subgrid-scale model. Experimental measurements of mean velocity, profiles of mass fractions, and temperature are used for comparison with the simulation data. The standard Smagorinsky model is considered the basic approach. Differences in the flow field statistics obtained in both subgrid-scale LES models are analyzed and discussed. The importance of taking the backscatter into account is highlighted.

Large-eddy-simulation of turbulent buoyant flow and conjugate heat transfer in a cubic cavity with fin ribbed radiators

Turbulent convective flow in a cubic cavity is a fundamental model observed in various processes that appeared in environmental and industrial applications. The turbulent fluctuations in the flow field, fluid-solid interaction/coupling, and the transient nature of the problem make it challenging to establish numerical modeling. The turbulent flow and convective heat transfer in a cubic cavity fixed with three fins are studied here. The numerical solutions are obtained through large-eddy simulation with Smagorinsky subgrid-scale model combined with conjugate heat transfer to incorporate temperature distribution in solid fins. The upper and lower walls of the enclosure are differently heated, while the lateral walls are adiabatic, and equally spaced conductive fins are located at the bottom surface. The solutions are initially compared with the numerical and experimental results for validation purposes. Successively, the model is applied to explore the impact of a material (copper) that makes up the horizontal wall on the flow field. We found that the heat transfer essentially alters the turbulent field, and the flow field becomes less homogeneous along the vertical direction. A number of streaky and coherent turbulent structures are found with varying magnitudes. The Q-criterion, second-invariant of the velocity-gradient tensor, predicted that strong vortices occur near the fins and in the surrounding regions of the cavity. Moreover, the energy (entropy) spectral, which plays a crucial role in engineering applications and turbulent theory, is also presented, showing the contribution of each frequency component to the velocity (temperature) variance at a given point. The velocity and temperature fields are found to be anti-symmetric, except close to the front and back walls. The major cause for this is the conducting bottom and fins, which produces thermal stratification in the cavity. The conducting bottom induces the locally unstable thermal stratification in the vicinity of the wall, which intensifies the turbulence as the flow advances toward the temperature-controlled boundaries. Further, the turbulent exchange in the central region is more responsible for the heat transfer than convection that occurs due to the differentially heated walls.

Acoustic Response of a Vibrating Elongated Cylinder in a Hydrodynamic Turbulent Flow

The present paper contains the results of the numerical analysis of the interaction between a Newtonian incompressible turbulent flow and a linear elastic slender body, together with the influence of the fluid–structure interaction (FSI) on the noise generation and propagation. The purpose is to evaluate the differences in term of acoustic pressure between the case where the solid body is rigid (infinite stiffness) and the case where it is elastic (finite stiffness). A partitioned and implicit algorithm with the arbitrary Lagrangian–Eulerian method (ALE) is used for the interaction between the fluid and solid. For the evaluation of the turbulent fluid motion, we use a large eddy simulation (LES) with the Smagorinsky subgrid scale model. The equation for the solid is solved through the Lagrangian description of the momentum equation and the second Piola–Kirchoff stress tensor. In addition, the acoustic analogy of Lighthill is used to characterize the acoustic source (the slender body) by directly using the fluid dynamic fields. In particular, we use the Ffowcs Williams and Hawkings (FW-H) equation for the evaluation of the acoustic pressure in the fluid medium. As a first numerical experiment, we analyze a square cylinder immersed in a turbulent flow characterized by two different values of stiffness: one infinite (rigid case) and one finite (elastic case). In the latter case, the body stiffness and mean flow velocity are such that they induce the lock-in phenomenon. Finally, we evaluate the differences in terms of acoustic pressure between the two different cases.

New criterion for characterization of thermal-saline jets discharged from thermal desalination plants

• The hydrodynamic pattern of inclined thermal-saline jets was examined using LES. • Jets pattern depended only on the ratio of salinity to thermal Froude numbers ( R ρ ). • Jets with R ρ lower than 1.2 behaved similar to the negatively buoyant jet. • Jets with R ρ in a range of 1.2-1.3 achieved better mixing characteristics. • Geometrical characteristics of jets became asymptotic for R ρ less than 0.7. More than 80% of desalination plants use the multi-stage flash (MSF) technology in the Persian Gulf and hence may have a severe irreversible impact on the marine environment. In the present study, geometrical, mixing, and turbulence characteristics of thermal-saline jets, similar to MSF effluents, are numerically investigated using the dynamic Smagorinsky sub-grid scale (SGS) model and UNESCO equation of state. For this purpose, two affecting dimensionless parameters are considered: (1) density ratio, which is thermal flux to salinity flux ratio, and (2) salinity Froude number. Examining the effects of density ratio reveals that the jet flow pattern only depends on the density ratio with a separating range of 1.2-1.3. In addition, increasing the density ratio increases the geometrical values of descending jets, reduces the geometrical values of ascending ones, and increases the descending jet's dilution before returning to the bed. Furthermore, geometrical values of descending jets show asymptotic behavior for density ratios less than 0.7. Eventually, turbulence characteristics of different jet flow patterns show that large turbulence structures are more explicit for the quasi-neutral scenario. The current results recommend that thermal desalination discharges similar to quasi-neutral jets with density ratios in a range of 1.2-1.3 achieve better mixing characteristics.

Geometry of deep and intermediate water breaking waves influenced by wind speed and direction

Wind effects on the evolution of a breaking wave group due to dispersive focusing are investigated using a two-phase flow Navier–Stokes solver. The Navier–Stokes equations are solved for both air and water, with the air–water interface captured by the Volume of Fluid method and the turbulence by the Smagorinsky subgrid-scale stress model. The two-phase model is first validated with the experimental measurements with and without following wind action. The following wind delays the breaking and shifts the breaking location downstream, and vice versa for the opposing wind. The wind-induced drift current is mainly responsible for these shifts of breaking time and location. The shift of breaking location and time is approximately linearly proportional to the wind speed (wind induced drift current) under weak winds, but the shift saturates under strong winds. The direct wind forcing, on the other hand, plays an increasingly larger role in the wave breaking process in the presence of stronger wind. It was found that the strong following wind forcing enhances the initiation of wave breaking, while the strong opposing wind forcing may change breaking type or suppress wave breaking of large intensity, such as plunging breaking. Accordingly, the wave shape at breaking onset is altered considerably under strong winds. The following wind increases the maximum wave height and wave skewness slightly. However, the opposing wind may also increase the maximum wave height initially because of the wind drift current induced upwave refocusing of the wave group. Eventually, stronger opposing wind decreases the wave height and wave skewness.

Turbulence suppression and regeneration in a magnetohydrodynamic duct flow due to influence of arbitrary electrically conductive walls

In the current study, we present a series of numerical simulations describing a turbulent magnetohydrodynamic flow subjected to a transverse magnetic field in a square duct with arbitrary electrically conductive walls. The characteristic flow and electromagnetic non-dimensional parameters (Reynolds and Hartmann number, respectively) were fixed, while the wall conductivity ratio (Cd) was varied from the perfectly electrically insulated (Cd = 0) to perfectly electrically conducting (Cd→∞). We have assumed the one-way coupling between the flow of an electrically conducting fluid and the imposed magnetic field. The influence of the electrically conducting walls was imposed by simulating additional finite solid domains coupled with the channel interior. The turbulence was simulated by applying the large eddy simulation approach with the dynamic Smagorinsky sub-grid scale model. The obtained results confirmed a significant impact of the conductivity of the surrounding walls on the flow and turbulence reorganization. We have observed that the initially fully developed turbulence regime was gradually suppressed in the 0≤Cd<0.15 range, while the fully laminarized state was obtained at Cd=0.15. We found that the process of turbulence suppression was accompanied by the appearance of the patterned turbulence phenomenon in the proximity of the walls parallel to the magnetic field direction. With a further increase in the wall conductivity parameter (0.15<Cd<∞), we have observed a complete turbulence regeneration. We found that this turbulence regeneration was caused by the local reorganization of the total current density loops near the electrically conducting walls.

A novel actuator line-immersed boundary (AL-IB) hybrid approach for wake characteristics prediction of a horizontal-axis wind turbine

The core idea of the actuator line (AL) model is to simplify the horizontal-axis wind turbine (HAWT) into a line with force distributed along the radial direction. The body force on the AL is employed to simulate the effect of the HAWT on the flow field, and the Navier-Stokes (N-S) equation is solved to obtain the aerodynamic and wake characteristics of the HAWT. Recently, the AL model has been comprehensively implemented in the investigation of wind turbine wakes. However, the existing standard AL model ignores or inaccurately describes the nacelle effects, which have been proven to considerably affect the accuracy of the near wake simulation. This paper develops an actuator line-immersed boundary (AL-IB) hybrid approach for the HAWT with high-accuracy and low-computational cost to address the physics problem underlying here. The wind turbine adopts the AL model instead of the body-fitted mesh method, and the nacelle is realized by the immersed boundary (IB) method. The large eddy simulation (LES) with a new localized dynamic Smagorinsky (LDS) sub-grid scale (SGS) model is adopted to model the turbulence to improve simulation accuracy of the near wake, thereby forming a set of high-fidelity numerical simulation framework of the HAWT wake. Firstly, the simulation accuracy of the AL-IB hybrid approach is validated by comparing the mean wake velocity profiles and turbulent kinetic energy (TKE) profiles of the HAWT with the experimental measurement results of the NTNU “Blind test 1”. Furthermore, the research is extended to the wake difference of the HAWT under two different numerical methods (AL and AL-IB). The results show that the solver developed based on AL-IB hybrid approach has higher accuracy than the standard AL model, which provides a feasible way for the refined numerical simulation of the large-scale wind farm.

Multiple-relaxation-time lattice Boltzmann method for three dimensional free-surface flows with multi-bubble model

Flow with bubbles is a commonly occurring phenomenon in nature and industrial applications. This study provides a multi-bubble model for the free surface lattice Boltzmann method (FSLBM) which can be used to simulate fluid flow with bubbles as well as their splitting and merging processes. FSLBM neglects the flow of gas and considers only the gas pressure, and thus simplifies the gas-liquid two-phase flow to a single-phase free surface. The compression of the bubble will influence its pressure and lead to movement, splitting, or merging processes within the bubble flow. The multi-bubble model considers the evolution of bubble's pressure by enhancing the model for free surface which simulates the behavior of gas-liquid interface inside the liquid. The Smagorinsky subgrid-scale model (SGS) and the more advanced multiple-relaxation-time (MRT) collision model is used for high Reynolds number. In this study, a bubble algorithm to handle the bubble splitting and merging without incurring significant computational costs is provided. The verification and analysis of this model are given by a comparison between both analytical solution and an experiment. Therefore, the multi-bubble as an extension of FSLBM can be used to solve a wider range of two-phase flow problems more efficiently, such as bubble formation, metal foaming process, and development in chemical reactors.

Dynamic LES of the magnetohydrodynamic flow in a square duct with the varied wall conductance parameters

The current study is focused on the magnetohydrodynamics and demonstrates how electrical conductivity of the wall can affect the turbulent flow in the square duct. Different variations of the boundary walls have been considered including arbitrary conductive walls. The Large Eddy Simulations method with the dynamic Smagorinsky sub-grid scale model have been used for the turbulent structures resolving. Results show the significant impact of the wall conductance parameters for both Hartmann and side walls.

Experimental and Numerical Study for Improved Understanding of Mixed-Convection Type of Flows in Turbine Casing Cavities During Shut-Down Regimes

Abstract Due to an increase in the power generation from renewable sources, steam and gas turbines will be required to adapt for more flexible operations with frequent start-ups and shut-downs to provide load leveling capacity. During shut-down regimes, mixed convection takes place with natural convection dominance depending on the operating conditions in turbine cavities. Buoyant flows inside the turbine that are responsible for nonuniform cooling leading to thermal stresses and compromise clearances directly limits the operational flexibility. Computational fluid dynamics (CFD) tools are required to predict the flow field during these regimes since direct measurements are extremely difficult to conduct due to the harsh operating conditions. Natural convection with the presence of cross-flow -mixed convection has not been extensively studied to provide detailed measurements. Since the literature lacks of research on such flows with real engine representative operating conditions for CFD validation, the confidence in numerical predictions is rather inadequate. This paper presents a novel experimental facility that has been designed and commissioned to perform very accurate unsteady temperature and flow field measurements in a simplified turbine casing geometry. The facility is capable of reproducing a wide range of Richardson, Grashof, and Reynolds numbers which are representative of engine realistic operating conditions. In addition, high fidelity, wall resolved large eddy simulation (LES) with dynamic Smagorinsky subgrid scale model has been performed. The flow field as well as heat transfer characteristics have been accurately captured with LES. Finally, the inadequacy of Reynolds-averaged Navier–Stokes (RANS) for the mixed type of flows has been highlighted.

Numerical study of the impact of glottis properties on the airflow field in the human trachea using V-LES

The influences of the profiles and cross-sectional areas of glottal aperture on the upper respiratory airway are investigated using an idealized cast-based mouth-throat model and three dimensional computational fluid dynamics (CFD). The open source CFD code OpenFOAM is employed. The transient flows are modeled using the very-large eddy simulation with the Smagorinsky sub-grid scale (SGS) model. Five different shapes of glottis are considered, including circular glottis with 100 %, 75 % and 50 % cross-sectional area and elliptic glottis with 75 % and 50 % cross-sectional area. Both instantaneous and averaged flow fields are analyzed. It is found that the variations of glottis have great impacts on the properties of downstream flow fields such as the secondary flow, laryngeal jet, recirculation zone, turbulent kinetic energy, and vortex. Evident impacts are observed in the region within 6 tracheal diameters downstream of the glottis. The profile of the glottis has more impacts on the laryngeal shape, while the cross-sectional area has more impacts on velocity of the laryngeal jet and turbulent intensity. It is concluded that both the glottal areas and profiles are critical for an idealized geometrical mouth-throat model.

Computation of a Compartment Fire with Smagorinsky Sub-Grid Scale Model

A fire tests using plywood crib as fire source was done in a cubical compartment to investigate the fire development and temperature distribution. The dimension of the experimental compartment was 4 m high, 4 m wide and 4 m length with a door opening of 2 m × 1 m wide located at one of the compartment wall. Several parameters were measured which includes fuel mass loss rate, compartment gas temperature, centerline doorway temperature, heat flux and wall surface temperature. Three-dimensional numerical simulations were performed using large eddy simulation with different values of Smagorinsky sub-grid scale constant. In order to accurately investigate the behavior of fire within the compartment by computational fluid dynamics (CFD), it is vital to study these Smagorinsky sub-grid scale constant. Numerically predicted results with various Smagorinsky sub-grid scale constant was compared with the physical results. It was found that the varying the Smagorinsky constant affect the numerical simulation results.

A fluid–structure interaction simulation on the wake-induced vibration of tandem cylinders with pivoted rotational motion

This paper predicts the wake-induced vibration of tandem cylinders with pivoted rotational or translational motion using the fluid–structure interaction technique. Large eddy simulation using a dynamic Smagorinsky subgrid-scale model is applied for the turbulent flow. Structural computation is applied to obtain the displacement of the downstream cylinder in the cross-flow direction. Conditions such as damping ratio, natural frequency, and mass ratio of pivoted rotational motion are the same as those of translational motion. The computational conditions are Re=3790, 8470 and 15 160, corresponding to U*=5.0, 11.2 and 20.0, respectively. The unsteady characteristics of lift, drag, and cross-flow motion of tandem cylinders are investigated. Distributions of pressure, λ2 criterion, vorticity, and streakline are also investigated. Finally, the energy harvesting capability of the pendulum system is compared with the translation system.

Non-hydrostatic model for internal wave generations and propagations using immersed boundary method

A non-hydrostatic model is developed to predict internal wave generations and propagations. The model employs a semi-implicit, fractional step algorithm to solve the governing equations based on the Cartesian grid system. Immersed boundary method is incorporated to deal with the complex geometry of uneven bottoms. The combination of the z-level vertical coordinate and the immersed boundary method enables the model to treat uneven bottoms and meanwhile to avoid numerical errors in the calculation of the baroclinic pressure force. To consider the effect of stratification, a variant of the Smagorinsky sub-grid scale model is employed to calculate the eddy viscosity and diffusivity. The capability of the model in resolving internal wave generation by tidal forcing over an idealized Gaussian-shaped topography is firstly validated by comparing the developed model with a terrain-following non-hydrostatic model. Then, two laboratory-scale test cases involving internal solitary wave propagations over variable topographies are considered. It can be found that the model captures the main characteristics of waveform evolution including internal hydraulic jump, wave breaking and waveform inversion. Thus, the proposed model provide an alternative to simulate internal wave generations and propagations.

High-fidelity simulations of gravity currents using a high-order finite-difference spectral vanishing viscosity approach

This numerical work investigates the potential of a high-order finite-difference spectral vanishing viscosity approach to simulate gravity currents at high Reynolds numbers. The method introduces targeted numerical dissipation at small scales through altering the discretisation of the second derivatives of the viscous terms in the incompressible Navier-Stokes equations to mimic the spectral vanishing viscosity (SVV) operator, originally designed for the regularisation of spectral element method (SEM) solutions of pure advection problems. Using a sixth-order accurate finite-difference scheme, the adoption of the SVV method is straightforward and comes with a negligible additional computational cost. In order to assess the ability of this high-order finite-difference spectral vanishing viscosity approach, we performed large-eddy simulations (LES) of a gravity current in a channelised lock-exchange set-up with our SVV model and with the well-known explicit static and dynamic Smagorinsky sub-grid scale (SGS) models. The obtained data are compared with a direct numerical simulation (DNS) based on more than 800 million mesh nodes, and with experimental measurements. A framework for the energy budget is introduced to investigate the behaviour of the gravity current. First, it is found that the DNS is in good agreement with the experimental data for the evolution of the front location and velocity field as well as for the stirring and mixing inside the gravity current. Secondly, the LES performed with less than 0.4% of the total number of mesh nodes compared to the DNS, can reproduce the main features of the gravity currents, with the SVV model yielding slightly more accurate results. It is also found that the dynamic Smagorinsky model performs better than its static version. For the present study, the static and dynamic Smagorinsky models are 1.8 and 2.5 times more expensive than the SVV model, because the latter does not require the calculation of explicit SGS terms in the Navier-Stokes equations nor spatial filtering operations.