Posteriori Tests Research Articles

On filtering in the viscous-convective subrange for turbulent mixing of high Schmidt number passive scalars

In the present work, we investigate the possibility of performing velocity-resolved, scalar-filtered (VR-SF) numerical simulations of turbulent mixing of high Schmidt number scalars, by using a Large Eddy Simulation (LES)-type filter in the viscous-convective subrange. The only requirement for this technique is the large scale separation between the Kolmogorov and Batchelor length scales, which is a direct outcome of the high Schmidt number of the scalar. The present a priori analysis using high fidelity direct numerical simulation data leads to two main observations. First, the missing triadic interactions between (resolved) velocity and (filtered-out) scalar modes in the viscous-convective subrange do not affect directly the large scales. Second, the magnitude of the subgrid term is shown to be extremely small, which makes it particularly susceptible to numerical errors associated with the scalar transport scheme. A posteriori tests indicate that upwinded schemes, generally used for LES in complicated geometries, are sufficiently dissipative to overwhelm any contribution from the subgrid term. This renders the subgrid term superfluous, and as a result, VR-SF simulations run without subgrid scalar flux models are able to preserve large scale transport characteristics with remarkable accuracy.

Subgrid-Scale Models for Large-Eddy Simulations of Shock-Boundary-Layer Interactions

Direct numerical simulation and large-eddy simulation of a flat-plate supersonic turbulent boundary layer interacting with an oblique incident shock wave are conducted for a priori and a posteriori assessments of subgrid-scale models. The incident shock is strong enough to generate a marginal separation in the boundary layer near the interaction region providing the subgrid-scale models with a nontrivial challenge. The governing equations for direct numerical simulation and large-eddy simulation are solved by a new seventh-order monotonicity-preserving scheme for inviscid fluxes and a sixth-order compact finite-difference scheme for the viscous terms. The effect of subgrid-scale stress term on the resolved velocity field is shown to be significant and shock-dependent. The subgrid-scale models tested include the mixed-time-scale model, the dynamic Smagorinsky model, the dynamic mixed model and a new dynamic model termed the compressible serial-decomposition model. A priori analysis indicate that the new dynamic model is more accurate than other subgrid-scale closures. A posteriori tests also indicate better predictions of direct numerical simulation results by the large-eddy simulation employing the compressible serial-decomposition model.

Evaluation of Low Reynolds Number Turbulence Models for an Open-Channel Flow over a Rough Bed Using LES Data

There are quite a few studies investigating low Reynolds number turbulence models for predicting the near-wall flow over smooth walls. However, analogous work over rough walls is sparse despite the fact that many flows of practical interest, particularly in geophysical flows and hydraulic engineering, are over rough walls. This paper presents a priori and a posteriori evaluations of low Reynolds number Reynolds-averaged Navier-Stokes (RANS)–based modeling approaches for flows over rough walls with the help of high-resolution large-eddy simulation (LES) data. The LES data allow the calculation of the vertical distribution of the turbulent kinetic energy, the dissipation rate, the specific dissipation rate, and the turbulent eddy viscosity, so that the assumptions inherent of RANS-based turbulence models can be tested a priori. A posteriori testing of the models through RANS simulations showed that the three low Reynolds turbulence models evaluated in this paper provide a fairly accurate prediction of the velocity profile, turbulent eddy viscosity, and wall shear stress.

An outlier locus relevant in habitat-mediated selection in an alpine plant across independent regional replicates

Habitat types can induce genetic responses in species and may drive adaptive differentiation and evolutionary divergence of populations. In this study, we aimed at detecting loci indicative of adaptation for different habitat types in the alpine plant Arabis alpina. We used a dataset consisting of A. alpina plants collected in scree, nutrient-rich and moist habitat types in two independent regional replicates of the European Alps (the Swiss and French Alps). Genome scans resulting in 825 amplified fragment length polymorphisms (AFLPs) followed by outlier analysis, i.e. looking for excessive differentiation between habitat types, after accounting for heterozygosity and population structure, was used to detect loci under divergent selection for habitat type within and across the alpine regions. The outlier analyses resulted in the detection of a consistent single outlier locus, which showed a higher fragment frequency in moist compared to the other habitat types in both alpine regions. In addition, a posteriori tests for hierarchical population structuring in the dataset did not detect signals confounding selection at this locus (i.e. signals of regional population structure). Thus, we consider this locus indicative of habitat-mediated selection, and we subsequently sequence-characterized and compared it to the Arabidopsis genome. The sequence was found to be a putative homologue to the SIT4 phosphatase-associated family protein. The detection of this locus in two alpine regions and the availability of its genome sequence make this locus a strong candidate worth further exploration in the habitat-mediated selection and genetic adaptation of natural populations in the alpine plant A. alpina.

Atmospheric water‐vapour profiling from passive microwave sounders over ocean and land. Part II: Validation using existing instruments

AbstractIn a companion article (Paper I), a water‐vapour retrieval algorithm has been developed using microwave sounding observations. An operational chain derived from this algorithm is being used for the Megha‐Tropiques mission, launched in autumn 2011. The water vapour is retrieved for clear and cloudy scenes, excluding precipitation cases, over ocean and land surfaces. By‐products are also calculated by the algorithm, including surface temperature and microwave emissivities over land.Evaluation of the water‐vapour products is the main objective of this article. The algorithm is tested using the HSB/AMSR‐E (resp. MHS/AMSU‐A) instruments on board the AQUA (resp. MetOp) platform, over the Tropics between ±30° in latitude. Results are compared with European Centre for Medium‐Range Weather Forecasts (ECMWF) analyses and data from radiosondes. The root‐mean‐square error for the total column water vapour is ∼5 kg m2 for both clear and cloudy scenes, compared with radiosondes over land. The atmospheric water‐vapour profile is retrieved for six atmospheric layers and the root‐mean‐square error is estimated to be lower than 20% in relative humidity, even for the lowest atmospheric layer over land. A posteriori validation tests on the brightness temperatures indicate an overall positive impact of the retrievals relative to a priori ECMWF analyses. Copyright © 2012 Royal Meteorological Society

Dynamic -equation model for large-eddy simulation of compressible flows

AbstractThis paper presents a dynamic one-equation eddy viscosity model for large-eddy simulation (LES) of compressible flows. The transport equation for subgrid-scale (SGS) kinetic energy is introduced to predict SGS kinetic energy. The exact SGS kinetic energy transport equation for compressible flows is derived formally. Each of the unclosed terms in the SGS kinetic energy equation is modelled separately and dynamically closed, instead of being grouped into production and dissipation terms, as in the Reynolds averaged Navier–Stokes equations. All of the SGS terms in the filtered total energy equation are found to reappear in the SGS kinetic energy equation. Therefore, these terms can be included in the total energy equation without adding extra computational cost.A prioritests using direct numerical simulation (DNS) of decaying isotropic turbulence show that, for a Smagorinsky-type eddy viscosity model, the correlation between the SGS stress and the model is comparable to that from the original model. Also, the suggested model for the pressure dilatation term in the SGS kinetic energy equation is found to have a high correlation with its actual value. Ina posterioritests, the proposed dynamic$k$-equation model is applied to decaying isotropic turbulence and normal shock–isotropic turbulence interaction, and yields good agreement with available experimental and DNS data. Compared with the results of the dynamic Smagorinsky model (DSM), the$k$-equation model predicts better energy spectra at high wavenumbers, similar kinetic energy decay and fluctuations of thermodynamic quantities for decaying isotropic turbulence. For shock–turbulence interaction, the$k$-equation model and the DSM predict similar evolutions of turbulent intensities across shocks, owing to the dominant effect of linear interaction. The proposed$k$-equation model is more robust in that local averaging over neighbouring control volumes is sufficient to regularize the dynamic procedure. The behaviour of pressure dilatation and dilatational dissipation is discussed through the budgets of the SGS kinetic energy equation, and the importance of the dilatational dissipation term is addressed.

An Inter-Laboratory Comparative Study of Serological Tools Employed in the Diagnosis ofBesnoitia besnoitiInfection in Bovines

Bovine besnoitiosis is considered an emerging chronic and debilitating disease in Europe. Many infections remain subclinical, and the only sign of disease is the presence of parasitic cysts in the sclera and conjunctiva. Serological tests are useful for detecting asymptomatic cattle/sub-clinical infections for control purposes, as there are no effective drugs or vaccines. For this purpose, diagnostic tools need to be further standardized. Thus, the aim of this study was to compare the serological tests available in Europe in a multi-centred study. A coded panel of 241 well-characterized sera from infected and non-infected bovines was provided by all participants (SALUVET-Madrid, FLI-Wusterhausen, ENV-Toulouse, IPB-Berne). The tests evaluated were as follows: an in-house ELISA, three commercial ELISAs (INGEZIM BES 12.BES.K1 INGENASA, PrioCHECK Besnoitia Ab V2.0, ID Screen Besnoitia indirect IDVET), two IFATs and seven Western blot tests (tachyzoite and bradyzoite extracts under reducing and non-reducing conditions). Two different definitions of a gold standard were used: (i) the result of the majority of tests ('Majority of tests') and (ii) the majority of test results plus pre-test information based on clinical signs ('Majority of tests plus pre-test info'). Relative to the gold standard 'Majority of tests', almost 100% sensitivity (Se) and specificity (Sp) were obtained with SALUVET-Madrid and FLI-Wusterhausen tachyzoite- and bradyzoite-based Western blot tests under non-reducing conditions. On the ELISAs, PrioCHECK Besnoitia Ab V2.0 showed 100% Se and 98.8% Sp, whereas ID Screen Besnoitia indirect IDVET showed 97.2% Se and 100% Sp. The in-house ELISA and INGEZIM BES 12.BES.K1 INGENASA showed 97.3% and 97.2% Se; and 94.6% and 93.0% Sp, respectively. IFAT FLI-Wusterhausen performed better than IFAT SALUVET-Madrid, with 100% Se and 95.4% Sp. Relative to the gold standard 'Majority of test plus pre-test info', Sp significantly decreased; this result was expected because of the existence of seronegative animals with clinical signs. All ELISAs performed very well and could be used in epidemiological studies; however, Western blot tests performed better and could be employed as a posteriori tests for control purposes in the case of uncertain results from valuable samples.

Sensitivity analysis of dense gas flow simulations to thermodynamic uncertainties

The paper investigates the sensitivity of numerically computed flow fields to uncertainties in thermodynamic models for complex organic fluids. Precisely, the focus is on the propagation of uncertainties introduced by some popular thermodynamic models to the numerical results of a computational fluid dynamics solver for flows of molecularly complex gases close to saturation conditions (dense gas flows). A tensorial-expanded chaos collocation method is used to perform both a priori and a posteriori tests on the output data generated by thermodynamic models for dense gases with uncertain input parameters. A priori tests check the sensitivity of each equation of state to uncertain input data via some reference thermodynamic outputs, such as the saturation curve and the critical isotherm. A posteriori tests investigate how the uncertainties propagate to the computed field properties and aerodynamic coefficients for a flow around an airfoil placed into a transonic dense gas stream.

Development of a new dynamic procedure for the Clark model of the subgrid-scale scalar flux using the concept of optimal estimator

Accurate prediction of a scalar advected by a turbulent flow is needed for various applications. In the framework of large-eddy simulation (LES), an accurate subgrid-scale (SGS) model for the subgrid-scale scalar flux has to be used. In this work, the performance of various dynamic SGS models is first evaluated by a priori tests through the concept of optimal estimator. Direct numerical simulation (DNS) in homogeneous isotropic turbulence is performed on 5123 grid points. Filtered quantities are extracted from the DNS data using a box or a spectral cut-off filter. The models’ accuracy is then evaluated in term of structural and functional performances, i.e., the model capacity to locally approximate the SGS unknown term and to reproduce its energetic action, respectively. It is shown that the Clark model has the best set of parameters to describe the SGS scalar flux. However, the classic dynamic procedure usually applied to compute the model coefficient leads to a large error. A new dynamic procedure is thus proposed to reduce this error. The results show that the new dynamic model leads to a good accuracy, which is not expectable from a model based only on the parameters of the classic dynamic Smagorinsky model. To better evaluate the improvement of the new dynamic procedure, a posteriori (large-eddy simulation) tests are performed for three different Schmidt numbers. It is shown that the new model allows to improve substantially the prediction of various scalar statistics.

A new dynamic formula for determining the coefficient of Smagorinsky model

The most common method to determine the coefficient of Smagorinsky model now is to employ the Germano identity, however it is too complex and expensive in numerical calculation. In this letter we propose a new dynamic formula for determining the coefficient, which is based on the Kolmogorov equation of filtered velocity in physical space. The simplified formula is quite easy to implement in calculation. It is then verified in both homogeneous isotropic turbulence and wall-bounded turbulence by A Priori and A Posteriori tests.

Quagga mussels ( Dreissena bugensis) as biomonitors of metal contamination: A case study in the upper St. Lawrence River

In this study, the utility of quagga mussels ( Dreissena bugensis) as biomonitors was investigated by measuring total concentrations of three trace metals, cadmium, copper, and zinc, in soft tissues. Quagga mussels were sampled from five sites along the upper St. Lawrence River, including one industrially influenced site, from 1999 through 2007. Mussels were collected from near-shore areas, divided into 5 size classes based on maximum shell length, and tissues were pooled for analysis of each size group. Two-way analysis of variance and a posteriori range tests were used to test for differences among sites along a distance gradient from the outflow of Lake Ontario and to examine inter-annual variability within and among sites. Cadmium concentrations were higher nearer the outflow of the lake. Copper concentrations varied among sites and years, but were generally highest near the industrial site. Zinc concentrations were relatively uniform, possibly reflecting internal regulation. Animal size measured as shell length was not an important factor in this section of the river, but warrants further consideration in a wider range of ecosystems and contaminant exposure levels. In general, concentrations of the three metals were not high compared to reports in the published literature for dreissenid mussels in contaminated environments. However, few studies have utilized quagga mussels rather than zebra mussels. The two species may differ in bioaccumulation patterns and may not be interchangeable as biomonitors. Further studies of bioaccumulation of contaminants by quagga mussels in a wider range of contaminant exposures would be useful particularly as quagga mussels displace zebra mussels in the Laurentian Great Lakes and the St. Lawrence River.

Assessment of large-eddy simulation in capturing preferential concentration of heavy particles in isotropic turbulent flows

Particle-laden turbulent flow is a typical non-equilibrium process characterized by particle relaxation time τp and the characteristic timescale of the flows τf, in which the turbulent mixing of heavy particles is related to different scales of fluid motions. The preferential concentration (PC) of heavy particles could be strongly affected by fluid motion at dissipation-range scales, which presents a major challenge to the large-eddy simulation (LES) approach. The errors in simulated PC by LES are due to both filtering and the subgrid scale (SGS) eddy viscosity model. The former leads to the removal of the SGS motion and the latter usually results in a more spatiotemporally correlated vorticity field. The dependence of these two factors on the flow Reynolds number is assessed using a priori and a posteriori tests, respectively. The results suggest that filtering is the dominant factor for the under-prediction of the PC for Stokes numbers less than 1, while the SGS eddy viscosity model is the dominant factor for the over-prediction of the PC for Stokes numbers between 1 and 10. The effects of the SGS eddy viscosity model on the PC decrease as the Reynolds number and Stokes number increase. LES can well predict the PC for particle Stokes numbers larger than 10. An SGS model for particles with small and intermediate Stokes numbers is needed to account for the effects of the removed SGS turbulent motion on the PC.

A general assessment method for subgrid-scale models in large-eddy simulation

A method combining the advantages of a priori and a posteriori testing approaches for subgrid-scale models in large-eddy simulation (LES) is proposed. It is implemented with various simple eddy viscosity models for decaying homogeneous turbulence. The method relies on the introduction of a restoring force in addition to the subgrid model. This force maintains the LES velocity field in the vicinity of the filtered velocity obtained from an accurately simulated flow. The analysis of this force provides new diagnostics on the efficiency of the subgrid-scale models.

A wavelet-based multiresolution approach to large-eddy simulation of turbulence

The wavelet-based multiresolution analysis (MRA) technique is used to develop a modelling approach to large-eddy simulation (LES) and its associated subgrid closure problem. The LES equations are derived by projecting the Navier–Stokes (N–S) equations onto a hierarchy of wavelet spaces. A numerical framework is then developed for the solution of the large and the small-scale equations. This is done in one dimension, for the Burgers equation, and in three dimensions, for the N–S problem. The proposed methodology is assessed in a priori tests on an atmospheric turbulent time series and on data from direct numerical simulation. A posteriori (dynamic) tests are also carried out for decaying and force-driven Burgers turbulence.

Large-eddy simulation of turbulent collision of heavy particles in isotropic turbulence

The small-scale motions relevant to the collision of heavy particles represent a general challenge to the conventional large-eddy simulation (LES) of turbulent particle-laden flows. As a first step toward addressing this challenge, we examine the capability of the LES method with an eddy viscosity subgrid scale (SGS) model to predict the collision-related statistics such as the particle radial distribution function at contact, the radial relative velocity at contact, and the collision rate for a wide range of particle Stokes numbers. Data from direct numerical simulation (DNS) are used as a benchmark to evaluate the LES using both a priori and a posteriori tests. It is shown that, without the SGS motions, LES cannot accurately predict the particle-pair statistics for heavy particles with small and intermediate Stokes numbers, and a large relative error in collision rate (up to 60%) may arise when the particle Stokes number is near StK=0.5. The errors from the filtering operation and the SGS model are evaluated separately using the filtered-DNS (FDNS) and LES flow fields. The errors increase with the filter width and have nonmonotonic variations with the particle Stokes numbers. It is concluded that the error due to filtering dominates the overall error in LES for most particle Stokes numbers. It is found that the overall collision rate can be reasonably predicted by both FDNS and LES for StK>3. Our analysis suggests that, for StK<3, a particle SGS model must include the effects of SGS motions on the turbulent collision of heavy particles. The spectral analysis of the concentration fields of the particles with different Stokes numbers further demonstrates the important effects of the small-scale motions on the preferential concentration of the particles with small Stokes numbers.

Quantification of thermodynamic uncertainties in real gas flows

A tensorial-expanded chaos collocation method is developed to take into account uncertainties on thermodynamic properties of complex organic substances. Precisely, we analyse the effect of uncertainties introduced by several thermodynamic models on the numerical results provided by a computational fluid dynamics solver for flows of molecularly complex gases close to saturation condition (dense gas flows). The tensorial-expanded chaos collocation method is used to perform both a priori and a posteriori tests on the output data generated by three popular thermodynamic models for dense gases with uncertain input parameters. A priori tests check the sensitivity of each equation of state to uncertain input data via some reference thermodynamic outputs, such as the saturation curve and the critical isotherm. A posteriori tests investigate how uncertainties propagate to the computed field properties and aerodynamic coefficients for a flow around an airfoil placed into a transonic dense gas stream.

Jump conditions for filtered quantities at an under-resolved discontinuous interface. Part 2: A priori tests

In order to study and validate the jump conditions established in part 1, we realize a priori tests thanks to the data of a 3D Direct Numerical Simulation (DNS) of a strongly deformable bubble in a spatially decaying turbulence. The complex interactions between interface and turbulence are fully resolved. An explicit filtering of the DNS has been employed to evaluate the filtered quantities and to check the potential of the models for two-phase flows in the Interface and Subgrid Scales (ISS) modeling case proposed in part 1. The ISS concept is our proposal of a two-phase equivalent for the one-phase Large Eddy Simulation (LES) modeling case with sharp-interfaces. In this concept, bubbles remain bigger than the mesh size. Due to the impossibility to define a filter equivalent to the matched asymptotic expansions, we only test the modeling of the equivalent interface transport (the momentum jump conditions are not tested in this article, but will deserve additional results in a posteriori tests). Because the closure of the transport equation of the under-resolved discontinuous interface requires more modeling assumptions than the closure of the momentum equation, we think that the most relevant test has been done. The a priori tests realized show excellent agreement between the ISS models and the real contributions.

An improved velocity increment model based on Kolmogorov equation of filtered velocity

The velocity increment (VI) model, which was introduced by Brun et al., is improved by employing the Kolmogorov equation of filtered velocity in this paper. This model has two different formulations: a dynamic formulation and a simplified constant form in high Reynolds number turbulence. A priori tests in isotropic turbulence and wall-bounded turbulence are performed. A posteriori tests of decaying turbulence and channel Poiseuille flow are made to testify the model performance, especially on the energy backscatter. The simple constant coefficient formulation has good performance, and avoids the ensemble average operation, which exists in other subgrid models. This constant improved VI model is particularly proposed in complicated large-eddy simulation projects.

A posteriori subgrid-scale model tests based on the conditional means of subgrid-scale stress and its production rate

Traditional a posteriori tests of subgrid-scale (SGS) models often compare large eddy simulation (LES) profiles of various statistics with measurements. In this study we propose and employ a new a posteriori test to study SGS model performance. We compare the conditional means of the LES-generated SGS stress and stress production rate conditional on the resolvable-scale velocity with measurements. These statistics must be reproduced by the SGS model for LES to correctly predict the one-point resolvable-scale velocity joint probability density function. Our tests using data obtained in convective atmospheric boundary layers show that the a posteriori results are consistent with our a priori tests based on the same conditional statistics. The strengths and deficiencies of the models observed here were also identified in our a priori tests. The remarkable consistency between the two types of tests suggests that statistical model tests based on the conditional SGS stress and its production rate are a highly capable approach for identifying specific model deficiencies and for evaluating SGS model performance in simulations.

Subgrid-scale contributions to Lagrangian time correlations in isotropic turbulence

The application of large-eddy simulation (LES) to particle-laden turbulence raises such a fundamental question as whether the LES with a subgrid scale (SGS) model can correctly predict Lagrangian time correlations (LTCs). Most of the currently existing SGS models are constructed based on the energy budget equations. Therefore, they are able to correctly predict energy spectra, but they may not ensure the correct prediction on the LTCs. Previous researches investigated the effect of the SGS modeling on the Eulerian time correlations. This paper is devoted to study the LTCs in LES. A direct numerical simulation (DNS) and the LES with a spectral eddy viscosity model are performed for isotropic turbulence and the LTCs are calculated using the passive vector method. Both a priori and a posteriori tests are carried out. It is observed that the subgrid-scale contributions to the LTCs cannot be simply ignored and the LES overpredicts the LTCs than the DNS. It is concluded from the straining hypothesis that an accurate prediction of enstrophy spectra is most critical to the prediction of the LTCs.