Eddy Viscosity Concept Research Articles

Numerical study of external turbulent flow

Flow around a cylinder on a fixed-bed open- channel is numerically studied. A CFD code is executed to analyze the flow fields and the kinetic energy field around the cylinder. A system of equations of two-dimensional and horizontal flow is obtained by the integration of the continuity and momentum equation for turbulent flow using (k -) standard model. The turbulent stresses are then expressed with the eddy-viscosity concept. The numerical simulation was done for four flows cases with different velocities. From the numerical results, the expected alteration of the flow field due to the presence of the cylinder is evident, notably the wake behind the cylinder. The measured velocities in the longitudinal and transversal directions and the kinetic energy are compared with those of the numerical simulation.

Physical/numerical duality of explicit/implicit subgrid-scale modelling

The development of implicit approaches has prompted debate on the actual usefulness of any explicit subgrid-scale modelling in large-eddy simulation. This question is addressed here by considering two generic turbulent flows: (i) the Taylor-Green vortex problem; (ii) the pipe flow. For both flow configurations, implicit modelling is found to overtake the very popular Smagorinsky model. To understand this robust observation, an analysis in the Fourier space is presented for the Taylor-Green vortex problem. The concept of spectral eddy viscosity, widely used in the pioneer work of Marcel Lesieur in two-point closure and subgrid-scale modelling, is revisited in a general framework based on explicit/implicit subgrid-scale modelling. In particular, the essentially anisotropic nature of implicit modelling is exhibited, as a favourable feature in terms of consistency with the computational mesh. Smagorinsky's model, considered as a generic explicit subgrid-scale model in the framework of Boussinesq's hypothesis, is found to be highly sensitive to numerical errors. Removing the latter is easy but makes computationally inefficient this type of explicit modelling. Comparisons between a priori and a posteriori spectral eddy viscosities show that neither Smagorinsky's model nor implicit modelling can mimic the expected spectral behaviour. Smagorinsky's model is observed to be weakly scale-selective with a poor ability to actually filter the solution. The feature of scale-selectivity is well replicated by implicit modelling which exhibits excellent capabilities for filtering. However, its lack of influence at the largest scales is against the expected behaviour for the spectral eddy viscosity at low wavenumber through the establishment of a non-zero plateau value. This lack of consistency of implicit LES could be overcome thanks to an extra explicit modelling but the attempt to mix Smagorinsky's model and implicit LES is not successful in this study. The potential of implicit large-eddy simulation is also exhibited for the accurate computation of near-wall turbulence inside a pipe flow despite the use of a regular Cartesian mesh with an immersed boundary method. Interestingly, the resulting coarse wall-normal resolution in the near-wall direction does not prevent the reliable prediction of statistical profiles up to the capture of subgrid-scale details. It is suggested that the regularisation associated with implicit modelling is a necessary condition to reach numerical accuracy. However, to faithfully represent the large-scale dynamics, present results confirm that non-local triad interactions must be taken into account as widely discussed in the inspiring textbook Lesieur [Turbulence in fluids. 4th ed. Springer; 2008] of Marcel Lesieur.

Favre-filtered LES-VOF of two-phase flows with eddy viscosity-based subgrid closure models: An a-posteriori analysis

Developing functional closure models for all the subgrid scale (SGS) physics in the large eddy simulation (LES) of turbulent two-phase flows is yet a challenging task due to the complicated turbulence-interface interactions. Our recent study (Saeedipour and Schneiderbauer, 2019) has revisited the classical eddy viscosity concept for the two-phase flows and proposed a new approach to include surface tension into the subgrid eddy viscosity. It has revealed an a-priori competence for the accurate simulation of the interfacial turbulence using the volume of fluid (VOF) method. The present study aims to exploit the potentials of this approach in an a-posteriori manner, which could be an important step towards the fully-functional LES models for two-phase flows. On the basis of the Favre-filtered governing equations, the corrected eddy viscosity model is adopted to close the convective, surface tension, and continuity SGS terms and establishes a functional LES-VOF approach. The models are implemented into an OpenFOAM-based geometric VOF solver. To perform the a-posteriori analysis two benchmark problems are considered: (i) a 2D turbulent phase inversion as also used for a-priori analysis, and (ii) a 3D freely-decaying, homogeneous isotropic turbulent flow in the presence of an initially-flat interface. The results reveal that compared to the conventional Smagorinsky model, the proposed LES-VOF method reveals a better performance in predicting the local turbulence characteristics as well as the energy spectra, particularly at flows with density contrasts. Also, the size distribution of the droplets shows a better agreement with the fully-resolved data. The a-posteriori analysis further unveils the importance of subgrid surface tension and the SGS residual term in the continuity equation in the development of the interfacial characteristics. The original contribution of this study lies in proposing a full LES approach for the two-phase flows with functional SGS models based on the revisited eddy viscosity concept. This method can be used for more accurate coarse-grid simulation of industrial problems with dispersed droplet regimes.

Analytical solution for depth-averaged velocity and boundary shear in a compound channel

Estimation of streamwise depth-averaged velocity and boundary shear stress are important requisites for modelling of river flows associated with flood events. Recently, many methods have emerged to predict these flow variables with great accuracy, but they provide unsatisfactory results in shear layer regions. This paper presents an improved methodology to predict depth-averaged velocity and bed shear stress for a straight compound channel flow. An analytical solution to the depth-integrated turbulent form of the Navier–Stokes equation is obtained. The transverse shear stress in the mixing region is modelled using an effective eddy viscosity concept that contains horizontal coherent structures and three-dimensional bottom turbulence. The secondary flow term is modelled by considering the log-law profile for streamwise velocity and half cosine curve for the transverse velocity component. The analytical solution is successfully applied to a wide range of experimental compound channels and field cases. The efficacy of the present solution has been successfully tested by comparing with observed values.

Spectral and modal energy transfer analyses of LES using the discontinuous Galerkin method and their application to the Variational Multiscale approach

In this work we perform a-priori analyses of the Discontinuous Galerkin (DG) Variational Multiscale (VMS) method for Large Eddy Simulation (LES). An analytical framework is introduced to study the ideal energy transfer between resolved and unresolved scales. The proposed framework is consistent with the discretization employed for the DG-LES simulations. The concept of modal eddy viscosity is also introduced which can be employed for the a-priori analysis of the DG-VMS method or spectral vanishing viscosity approaches. The developed framework is then applied to the analysis of the energy transfer in DG-LES by employing a DNS database of the Taylor-Green Vortex (TGV) at Re = 5000, 20000 and 40000. A-priori analyses are carried out for the Vreman [1] and all-all [2] variants of the DG-VMS approach. The performed analysis demonstrates that when the DG-LES resolution limit falls at the beginning of the dissipation range the assumption of large scales free of interaction with the unresolved scales is valid and the DG-VMS approach can replicate the ideal SGS dissipation spectrum. For coarser resolutions, typical of LES at high Reynolds numbers, the DG-VMS approach is unable to replicate the ideal energy transfer mechanism at the large-resolved scales. It is shown, a-priori, that a more accurate agreement can be obtained by employing a mixed Smagorinsky and DG-VMS approach with a fixed value of the scale-fraction parameter.

Statistical Lyapunov Theory Based on Bifurcation Analysis of Energy Cascade in Isotropic Homogeneous Turbulence: A Physical–Mathematical Review

This work presents a review of previous articles dealing with an original turbulence theory proposed by the author and provides new theoretical insights into some related issues. The new theoretical procedures and methodological approaches confirm and corroborate the previous results. These articles study the regime of homogeneous isotropic turbulence for incompressible fluids and propose theoretical approaches based on a specific Lyapunov theory for determining the closures of the von Kármán–Howarth and Corrsin equations and the statistics of velocity and temperature difference. While numerous works are present in the literature which concern the closures of the autocorrelation equations in the Fourier domain (i.e., Lin equation closure), few articles deal with the closures of the autocorrelation equations in the physical space. These latter, being based on the eddy–viscosity concept, describe diffusive closure models. On the other hand, the proposed Lyapunov theory leads to nondiffusive closures based on the property that, in turbulence, contiguous fluid particles trajectories continuously diverge. Therefore, the main motivation of this review is to present a theoretical formulation which does not adopt the eddy–viscosity paradigm and summarizes the results of the previous works. Next, this analysis assumes that the current fluid placements, together with velocity and temperature fields, are fluid state variables. This leads to the closures of the autocorrelation equations and helps to interpret the mechanism of energy cascade as due to the continuous divergence of the contiguous trajectories. Furthermore, novel theoretical issues are here presented among which we can mention the following ones. The bifurcation rate of the velocity gradient, calculated along fluid particles trajectories, is shown to be much larger than the corresponding maximal Lyapunov exponent. On that basis, an interpretation of the energy cascade phenomenon is given and the statistics of finite time Lyapunov exponent of the velocity gradient is shown to be represented by normal distribution functions. Next, the self–similarity produced by the proposed closures is analyzed and a proper bifurcation analysis of the closed von Kármán–Howarth equation is performed. This latter investigates the route from developed turbulence toward the non–chaotic regimes, leading to an estimate of the critical Taylor scale Reynolds number. A proper statistical decomposition based on extended distribution functions and on the Navier–Stokes equations is presented, which leads to the statistics of velocity and temperature difference.

Local-Variable-Based Model for Hypersonic Boundary Layer Transition

Based on the numerical study of the existing model, certain inconsistencies of the model were first allocated. It was found that the second-mode instability dominating the transition process in hypersonic boundary layers was not simulated properly by the model, and a single transport equation for total fluctuating kinetic energy would make the model fail to be self-consistent. To eliminate these discrepancies, a laminar kinetic energy transport equation was developed in terms of local variables. Then, a time scale correction function capable of reproducing the hypersonic transition process dominated by the second-mode instability was constructed. In addition, the transport equation for the intermittency factor, in which the self-consistent production and dissipation terms were constructed, was also revised. On this basis, the transport equations for the laminar kinetic energy and intermittency factor were coupled with the shear stress transport model through the concept of effective turbulent eddy viscosity to form a local-variable-based model for hypersonic boundary layer transition. Finally, hypersonic transition flows over a flat plate and a straight cone are employed to test and verify the model. Numerical results illustrate that both the transition onset and the length of the transition region predicted by the model agree well with the experimental data.

A Thermoelastohydrodynamic Analysis for the Static Performance of High-Speed—Heavy Load Tilting-Pad Journal Bearing Operating in the Turbulent Flow Regime and Comparisons to Test Data

Abstract Tilting-pad journal bearings (TPJBs) ensure rotordynamic stability that could otherwise produce dangerously large amplitude rotor oil-whirl/whip motions in high-speed rotating machinery. Currently, highly efficient turbo compressors demand an ever increasing rotor surface speed and specific load on its support bearings. The accurate prediction of bearing performance is vital to guarantee reliable products, specifically with regard to reducing maximum bearing pad temperature and drag power losses, and operating with the least flow rate while still maximizing load capacity. The hydrodynamic pressure and heat generation in an oil film acting on a bearing pad produce significant mechanical and thermal deformations that change the oil film geometry (clearance and preload) to largely affect the bearing performance, static, and dynamic. In addition, a high surface speed bearing often operates in the turbulent flow regime that produces a notable increase in power loss and a drop in maximum pad temperature. This paper details a thermoelastohydrodynamic (TEHD) analysis model applied to TPJBs, presents predictions for their steady-load performance, and discusses comparisons with experimental results to validate the model. The test bearing has four pads with a load between pads configuration; its length L = 76.2 mm and shaft diameter D = 101.6 mm (L/D = 0.75). The rotor top speed is 22.6 krpm, i.e., 120 m/s surface speed, and the maximum specific load is 2.94 MPa for an applied load of 23 kN. The test procedure records shaft speed and applied load, oil supply pressure/temperature and flow rate, and also measures the pads' temperature and shaft temperature, as well as the discharge oil (sump) temperature. The TEHD model couples a generalized Reynolds equation for the hydrodynamic pressure generation with a three-dimensional energy transport equation for the film temperature. The pad mechanical deformation due to pressure utilizes the finite elemental method, whereas an analytical model estimates thermally induced pad crowning deformations. For operation beyond the laminar flow regime, the analysis incorporates the eddy viscosity concept for fully developed turbulent flow operation. Current predictions demonstrate the influence of pressure and temperature fields on the pads mechanical and thermally induced deformation fields and also show static performance characteristics such as bearing power loss, flow rate, and pad temperatures. The comparisons of test results and analysis results reveal that turbulent flow effects significantly reduce the pads' maximum temperature while increasing the bearing power loss. Turbulent flow mixing increases the diffusion of thermal energy and makes more uniform the temperature profile across the film.

Wall-roughness eddy viscosity for Reynolds-averaged closures

An approach to modeling the effect of rough surfaces on turbulent boundary-layer flow is proposed and developed. It is based on the concept of a rough-wall eddy viscosity, in which the pressure and viscous drag forces which arise on account of flow past roughness elements are recast as an equivalent viscous shear force within the roughness sublayer at the surface. This shear force is modeled as the wall-roughness eddy viscosity and carries information on both the flow Reynolds number and the roughness height. The modeling approach is developed and evaluated as part of a k–ε closure. When the wall-roughness eddy viscosity is modeled in proportion to (ks+)3/4, where ks+=ksuτ/ν and is the sand-grain roughness in wall units, it yields predictions of drag coefficients which are in excellent agreement with those from reference data for flow in rough-walled pipes, over a wide range of surface-roughness heights and Reynolds numbers. Its predictions are also in good agreement with experimental data for zero and favorable pressure gradient boundary layers over fully-rough surfaces.

High-Order Boussinesq-Type Model for Integrated Nearshore Dynamics

AbstractA two-dimensional high-order Boussinesq-type model was derived to simulate wave propagation and relevant processes in the nearshore zone. Because of its enhanced nonlinear character, the model can describe more accurately the amplitude dispersion compared to its weakly nonlinear counterpart. Extension to the surf zone was accomplished using the eddy-viscosity concept for simulating breaking waves. Swash-zone dynamics were simulated by applying a modified narrow-slot technique. Bottom friction and subgrid turbulent mixing were also incorporated. The model can estimate the wave-induced current field, including the undertow effect. The numerical model relied on a generalized multistep predictor-corrector scheme, and the waves were generated using the source function method. Both the one-horizontal-dimensional (1DH) and two-horizontal-dimensional (2DH) versions were validated against a variety of experimental tests, including regular and irregular wave propagation and breaking on plane beaches and sub...

Circular Far-Wake Flow behind a Sphere: Solutions to the Second Order

AbstractThe theory of hydrodynamic phenomenon of the axisymmetric circular far-wake flow behind a sphere is revisited in this study by the generalized similarity solution of the governing momentum equations to obtain the solutions to the second order in respect of the inverse distance from the sphere center. In case of a laminar wake, the nonlinear equation is derived from the Navier–Stokes equations; while in case of a turbulent wake, it is obtained from the Reynolds averaged Navier–Stokes (RANS) equations and the eddy viscosity concept. The first-order Oseen-type linearization yields solutions well known in the literature, but the second-order solutions obtained in this study are novel.

Coupling of a free wake vortex ring near-wake model with the Jensen and Larsen far-wake deficit models

This paper presents a simple physical model to improve the currently used far-wake deficit models in the wind industry. The main improvement is deemed on the determination of the wake deficit in the near-wake. A Vortex Ring Model (VRM) is used to calculate the induced velocities in the near-wake, which are then coupled to the Jensen far-wake model and the Larsen far-wake model based on the concept of Eddy Viscosity (EV). The inviscid near-wake VRM is based on the shedding of discrete tip vortex rings released from a uniformly loaded actuator disc. The model is validated against wind tunnel measurements from experiments with a two- bladed turbine and a circular metal mesh with a uniform porosity to represent an actuator disc. The VRM shows a good agreement with the experimental data with respect to the wake deficit evolution. The VRM is coupled with two well-known engineering type far-wake models: the Jensen and Larsen wake deficit models. The results of the coupling of the VRM and the more elaborated Larsen far-wake model are compared against a 3D Large Eddy Simulation (LES) CFD model. This comparison shows the effect of different near-wake models on the development of centreline velocities in the far-wake. The centreline velocity deficit predicted by the VRM-Larsen model more closely matches LES calculations in comparison with the reference Larsen model.

Buoyancy-induced turbulence in a tilted pipe

AbstractNumerical simulation is used to document the statistical structure and better understand energy transfers in a low-Reynolds-number turbulent flow generated by negative axial buoyancy in a long circular tilted pipe under the Boussinesq approximation. The flow is found to exhibit specific features which strikingly contrast with the familiar characteristics of pressure-driven pipe and channel flows. The mean flow, dominated by an axial component exhibiting a uniform shear in the core, also comprises a weak secondary component made of four counter-rotating cells filling the entire cross-section. Within the cross-section, variations of the axial and transverse velocity fluctuations are markedly different, the former reaching its maximum at the edge of the core while the latter two decrease monotonically from the axis to the wall. The negative axial buoyancy component generates long plumes travelling along the pipe, yielding unusually large longitudinal integral length scales. The axial and crosswise mean density variations are shown to be respectively responsible for a quadratic variation of the crosswise shear stress and density flux which both decrease from a maximum on the pipe axis to near-zero values throughout the near-wall region. Although the crosswise buoyancy component is stabilizing everywhere, the crosswise density flux is negative in some peripheral regions, which corresponds to apparent counter-gradient diffusion. Budgets of velocity and density fluctuations variances and of crosswise shear stress and density flux are analysed to explain the above features. A novel two-time algebraic model of the turbulent fluxes is introduced to determine all components of the diffusivity tensor, revealing that they are significantly influenced by axial and crosswise buoyancy effects. The eddy viscosity and eddy diffusivity concepts and the Reynolds analogy are found to work reasonably well within the central part of the section whereas non-local effects cannot be ignored elsewhere.

Half-Order Stable Boundary-Layer Parametrization Without the Eddy Viscosity Approach for Use in Numerical Weather Prediction

A turbulence parametrization for wind speed in the stable boundary layer consisting of a single empirical parameter is proposed without the use of the eddy viscosity concept or turbulent kinetic energy equation. Instead, a drag-coefficient-type formulation as a function of the bulk Richardson number has been found to be able to reproduce observed stable boundary-layer wind speeds as effectively as a model based on the eddy viscosity approach. The advantage of this simpler approach is that the model can, in theory, be modified more easily for certain applications, such as the effects of large-scale wind parks on mesoscale meteorology.

Spectral eddy viscosity of stratified turbulence

AbstractThe spectral eddy viscosity (SEV) concept is a handy tool for the derivation of large-eddy simulation (LES) turbulence models and for the evaluation of their performance in predicting the spectral energy transfer. We compute this quantity by filtering and truncating fully resolved turbulence data from direct numerical simulations (DNS) of neutrally and stably stratified homogeneous turbulence. The results qualitatively confirm the plateau–cusp shape, which is often assumed to be universal, but show a strong dependence on the test filter size. Increasing stable stratification not only breaks the isotropy of the SEV but also modifies its basic shape, which poses a great challenge for implicit and explicit LES methods. We find indications that for stably stratified turbulence it is necessary to use different subgrid-scale (SGS) models for the horizontal and vertical velocity components. Our data disprove models that assume a constant positive effective turbulent Prandtl number.

Analysis of Empirical Constant of Eddy Viscosity by Zero- and One-Equation Turbulence Model in Wake Simulation

In this paper, the wakes behind a square cylinder were simulated using two kinds of different turbulence models for the eddy viscosity concept such as the zero- and the one-equation model in which the former is the mixing length model and the latter is the k-equation model. For comparison between numerical and analytical solutions, we employed three skill assessments: the correlation coefficient(r) for the similarity of the wake shape, the error of maximum velocity difference(EMVD) for the accuracy of wake velocity and the ratio of drag coefficient(RDC) for the pressure distribution around the structure. On the basis of the numerical results, the feasibility of each model for wake simulation was discussed and a suitable value for the empirical constant was suggested in these turbulence models. The zero-equation model, known as the simplest turbulence model, overestimated the EMVD and its absolute mean error(AME) for r , EMVD and RDC was ranging from 20.3 % to 56.3 % for all test. But the AME by the one-equation model was ranging from 3.4 % to 19.9 %. The predicted values of the one-equation model substantially agreed with the analytical solutions at the empirical mixing length scale L+0.6b 1/2 with the AME of 3.4 %. Therefore it was concluded that the one-equation model was suitable for the wake simulation behind a square cylinder when the empirical constant for eddy viscosity would be properly chosen.

Analysis of Flow Separation Using a Local Frame Axis: Application to the Open-Channel Bifurcation

The motivation for the present work comes from the fact that a few recent publications describing separation flows report a counter-gradient diffusion phenomenon (CDP) along the separating streamline. This CDP is related to (1) a change of sign of the Reynolds shear stress near the separating point and (2) an opposite sign between the Reynolds shear stress and the mean shear rate, leading to a negative eddy-viscosity coefficient. Such CDP is only reported for configurations where the angle between the separating streamline and the main flow is large (referred to as group 1), whereas no CDP was reported for low angle configurations (referred to as group 2). All these flows were analyzed using Cartesian or curvilinear frame axes. The aim of the present paper is to propose a more intuitive frame for analysis, namely the Serret-Frenet frame axis based on the local flow direction, for which the CDP disappears for group 1 flow configurations and that highly improves the characterization of the mixing layer. The recirculation zone occurring in the lateral branch of an open-channel bifurcation is chosen as a separating flow configuration belonging to group 1 and measured using particle image velocimetry (PIV). The characteristics of the mean flow and of the horizontal Reynolds stress are first analyzed using a Cartesian frame axis, to retrieve the CDP, for which extension is enhanced compared with the literature cases. Then, the local Serret-Frenet frame axis is introduced and used for a second analysis of the data. The flow characteristics at the interface between the main flow and the recirculation zone accurately match the characteristics of the well-documented mixing layers available in the literature. Moreover, the eddy-viscosity concept nicely applies using this Serret-Frenet frame axis. A simple geometrical analysis is finally performed to confirm that the negative eddy-viscosity coefficient obtained when using a Cartesian frame axis is only attributable to a nonadequate frame of analysis.

A modular RANS approach for modelling laminar–turbulent transition in turbomachinery flows

In this study we propose a laminar–turbulent transition model, which considers the effects of the various instability modes that exist in turbomachinery flows. This model is based on a K–ω–γ three-equation eddy-viscosity concept with K representing the fluctuating kinetic energy, ω the specific dissipation rate and γ the intermittency factor. As usual, the local mechanics by which the freestream disturbances penetrate into the laminar boundary layer, namely convection and viscous diffusion, are described by the transport equations. However, as a novel feature, the non-local effects due to pressure diffusion are additionally represented by an elliptic formulation. Such an approach allows the present model to respond accurately to freestream turbulence intensity properly and to predict both long and short bubble lengths well. The success in its application to a 3-D cascade indicates that the mixed-mode transition scenario indeed benefits from such a modular prediction approach, which embodies current conceptual understanding of the transition process.

Near-Wake Turbulent Flow Structure and Mixing Length Downstream of a Fractal Tree

In order to study the turbulence structure behind a multiscale tree-like element in a boundary layer, detailed particle image velocimetry measurements are carried out in the near-wake of a fractal-like tree. The tree is a pre-fractal with five generations, each consisting of three branches and a scale-reduction factor of 1/2 between consecutive generations. Detailed mean velocity and turbulence stress profiles are documented, as well as their downstream development. Scatter plots of mean velocity gradient (transverse shear in the wake) and Reynolds shear stress exhibit a good linear relation at all locations in the flow. Therefore, in the transverse direction of the wake evolution, the data support the Boussinesq eddy-viscosity concept. The measured mixing length increases with streamwise distance, in agreement with classic wake expansion rates. Conversely, the measured eddy viscosity and mixing length in the transverse direction decrease with increasing elevation, which differs from the behaviours measured in the vertical direction in traditional boundary layers or in canopy flows studied before. In order to find an appropriate single length scale to describe the wake evolution behind a multiscale object, two models are proposed, based on the notion of superposition of scales. One approach is based on the radial spectrum of the object while the second is based on its length-scale distribution evaluated using fractal geometry tools. Both proposed models agree well with the measured mixing length. The results suggest that information about multiscale clustering of branches must be incorporated into models of the mixing length for flows through single or sparse canopies of multiscale trees.

The influence of advection schemes and turbulence closure models on drag coefficient calculation around a circular cylinder at high Reynolds number

Different advection schemes and two-equation turbulence closure models based on eddy viscosity concept are used to compute the drag coefficient around a circular cylinder at high Reynolds number (106). The numerical results from these simulations are compared with each other and with experimental data in order to evaluate the performance of different combinations of advection scheme and two-equation turbulence model. The separate contributions from form drag and friction drag are also analyzed. The computational results show that the widely used standard k-ɛ turbulence closure is not suitable for such kind of study, while the other two-equation turbulence closure models produce acceptable results. The influence of the different advection schemes on the final results are small compared to that produced by the choice of turbulence closure method. The present study serves as a reference for the choice of advection schemes and turbulence closure models for more complex numerical simulation of the flow around a circular cylinder at high Reynolds number.