Interacting errors in large-eddy simulation: a review of recent developments

The accuracy of large-eddy simulations is limited, among others, by the quality of the subgrid parameterisation and the numerical contamination of the smaller retained flow structures. We review the effects of discretisation and modelling errors from two different perspectives. We first show that spatial discretisation induces its own filter and compare the dynamic importance of this numerical filter to the basic large-eddy filter. The spatial discretisation modifies the large-eddy closure problem as is expressed by the difference between the discrete 'numerical stress tensor' and the continuous 'turbulent stress tensor'. This difference consists of a high-pass contribution associated with the specific numerical filter. Several central differencing methods are analysed and the importance of the subgrid resolution is established. Second, we review a database approach to assess the total simulation error and its numerical and modelling contributions. The interaction between the different sources of error is shown to lead to their partial cancellation. From this analysis one may identify an 'optimal refinement strategy' for a given subgrid model, discretisation method and flow conditions, leading to minimal total simulation error at a given computational cost. We provide full detail for homogeneous decaying turbulence in a 'Smagorinsky fluid'. The optimal refinement strategy is compared with the error reduction that arises from grid refinement of the dynamic eddy-viscosity model. The main trends of the optimal refinement strategy as a function of resolution and Reynolds number are found to be adequately followed by the dynamic model. This yields significant error reduction upon grid refinement although at coarse resolutions significant error levels remain. To address this deficiency, a new successive inverse polynomial interpolation procedure is proposed with which the optimal Smagorinsky constant may be efficiently approximated at a given resolution. The computational overhead of this optimisation procedure is shown to be well justified in view of the achieved reduction of the error level relative to the 'no-model' and dynamic model predictions

Specifics

In all these examples there appears to be mismatch between the position at which an indefinite appears and its preferred interpretation. Following many of the more recent contributions to the literature, I will assume that this is the hallmark of specificity (e.g. Ahusch 1994, Reinhart 1997, Winter 1997, van Geenhoven 1998). Such mismatches are not the norm: indefinites are often interpreted in situ, and there is some reason for taking this to be the default option. The reason is that comparatively 'neutral', i.e. semantically attenuate, indefinites have a preference for in situ readings [...]

Regularization modeling for large-eddy simulation of diffusion flames

We analyze the evolution of a diffusion flame in a turbulent mixing layer using large-eddy simulation. The large-eddy simulation includes Leray regularization of the convective transport and approximate inverse filtering to represent the chemical source terms. The Leray model is compared to the more conventional dynamic mixed model. The location of the flame-center is defined by the 'stoichiometric' interface. Geometrical properties such as its surface-area and wrinkling are characterized using an accurate numerical level-set quadrature method. This allows to quantify flame-properties as well as turbulence modulation effects due to coupling between combustion and turbulent transport. We determine the active flame-region that is responsible for the main part of the chemical conversion in the flame and compare direct and large-eddy simulation predictions

The feeding and breeding ecology of little blue penguins (Eudyptula minor) from Tiritiri Matangi Island, New Zealand : a thesis submitted in partial fulfilment of the requirements for the degree of Master of Science in Conservation Ecology, Massey University

At present the New Zealand populations of Little Blue Penguins (LBP: Eudyptula minor) are classified as 'Threatened' and in 'Gradual Decline' by the Department of Conservation. Effective conservation management of the North Island sub-species requires an understanding of the factors affecting their survival and breeding success. There is little information on the breeding ecology of the E. minor, especially in the North Island of New Zealand. The overall goal of this study was to establish baseline data on a North Island population of LBP in New Zealand. The aims of this study were to 1) identify population demographics, 2) quantify breeding success and identify abiotic and biotic parameters influencing nesting success, 3) identify feeding ecology based on diet and trophic level assessment, and 4) identify cause of death and underlying patterns associated with mass mortalities of the LBP species. Breeding success was quantified by monitoring the nesting activity of 87 nesting attempts during the 2005/06 breeding season. Nest monitoring also involved identifying risks associated with both the egg and chick stage. Diet analysis involved comparing stomach regurgitation samples and isotope samples of feathers spanning a 120 year period. The cause of death for the mass occurrence of beach wrecked birds found during 2005/06 was established through necropsies and histological tests. The major cause of death was compared to patterns of past beach wreck events that has occurred in New Zealand over a 33 year period, obtained through the Ornithological Society of New Zealand. Where possible, both short- and long-term comparisons were made to establish a sound understanding of the key factors that are influencing breeding success, foraging, and survival. Results showed that 2005/06 was a poor breeding year which was the result of a large number of nest desertions. Furthermore, analysis of stable isotopes shows that the LBP have been feeding at low trophic levels over the past 120 years and that 2005 was significantly lower in carbon levels suggesting a low year of marine productivity. The largest cause of death associated with mass beach wrecks was starvation. Analysis of past beach wrecks suggest that during the year LBP are at a greater risk of death after the breeding season, after moult, and during winter which are energetically expensive periods. A more long-term study is required to identify the trends in LBP breeding success and to ascertain the primary reason as to why they are unable to obtain enough food. Seabirds are increasingly being used as biological indicators since they are largely influenced by changes associated with the marine environment. The use of LBP as biological indicators may have limitations depending on the parameters being used. However stable isotope measures may be one of the easiest methods to achieve this and allows for reconstruction of past ecological histories through analysis of historical tissues

Buoyant turbulent mixing in shear layers

Buoyancy effects in unstably stratified mixing layers express themselves through gravity currents of heavy fluid which propagate in an ambient lighter fluid. These currents are encountered in numerous geophysical flows, industrial safety and environmental protection issues. During transition to turbulence a strong distortion of the separating interface between regions containing `heavy' or `light' fluid arises. The complexity of this interface will be used to monitor the progress of the mixing. We concentrate on the enhancement of surface-area and `surface-wrinkling' of the separating interface as a result of gravity-effects. We also show that this process can be simulated quite accurately using large-eddy simulation with dynamic subgrid modeling. However, the subgrid resolution, defined as the ratio between filter-width Delta and grid-spacing h, should be sufficiently high to avoid contamination due to spatial discretization error effects.Comment: 4 pages, 5 figures; to appear in Proceedings ETC9, Eds: I.P. Castro and P.E. Hancock, CIMNE, Barcelona, 200

The reptating rope model: Viscometric functions for concentrated polymer solutions and melts in shear flow

The viscometric functions for shear flow as predicted by the inextensible reptating rope model have been analysed numerically and analytically. The results obtained are compared with the predictions of the Curtiss—Bird theory. It is shown that if the correlation length of the rope is small as compared to its contour length significant deviations from the Curtiss—Bird theory are obtained. Results are presented for: (a) the onset of shear flow, (b) steady state shear flow and (c) small amplitude oscillatory shear flow

Magnitude control of commutator errors

Non-uniform filtering of the Navier-Stokes equations expresses itself, next to the turbulent stresses, in additional closure terms known as commutator errors. These terms require explicit subgrid modeling if the non-uniformity of the filter is sufficiently pronounced. We derive expressions for the magnitude of the mean flux, the turbulent stress flux and the commutator error for individual Fourier modes. This gives rise to conditions for the spatial variations in the filter-width and the filter-skewness subject to which the magnitude of the commutator errors can be controlled. These conditions are translated into smoothness requirements of the computational grid, that involve ratios of first -, second - and third order derivatives of the grid mapping