J. Andrzej Domaradzki

An adaptive local deconvolution method for implicit LES

The adaptive local deconvolution method (ALDM) is proposed as a new nonlinear discretization scheme designed for implicit large-eddy simulation (ILES) of turbulent flows. In ILES the truncation error of the discretization of the convective terms functions as a subgrid-scale model. Therefore, the model is implicitly contained within the discretization, and an explicit computation of model terms becomes unnecessary. The discretization is based on a solution-adaptive deconvolution operator which allows to control the truncation error. Deconvolution parameters are determined by an analysis of the spectral numerical viscosity. An automatic optimization based on an evolutionary algorithm is employed to obtain a set of parameters which results in an optimum spectral match for the numerical viscosity with theoretical predictions for isotropic turbulence. Simulations of large-scale forced and decaying three-dimensional homogeneous isotropic turbulence show an excellent agreement with theory and experimental data and demonstrate the good performance of the implicit model. As an example for transitional flows, instability and breakdown of the three-dimensional Taylor-Green vortex are considered. The implicit model correctly predicts instability growth and transition to developed turbulence. It is shown that the implicit model performs at least as well as established explicit models.

A subgrid-scale model based on the estimation of unresolved scales of turbulence

A new method for large eddy simulations is described and evaluated. In the proposed method the primary modeled quantity is the unfiltered velocity field appearing in the definition of the subgrid-scale stress tensor. An estimate of the unfiltered velocity is obtained by expanding the resolved large-scale velocity field to subgrid-scales two times smaller than the grid scale. The estimation procedure consists of two steps. The first step utilizes properties of a filtering operation and the representation of quantities in terms of basis functions such as Fourier polynomials. In the second step, the phases associated with the newly computed smaller scales are adjusted in order to correspond to the small-scale phases generated by nonlinear interactions of the large-scale field. The estimated velocity field is expressed entirely in terms of the known, resolved velocity field without any adjustable constants. The modeling procedure is evaluated in a priori analyses using direct numerical simulation results of c...

Local energy transfer and nonlocal interactions in homogeneous, isotropic turbulence

Detailed computations were made of energy transfer among the scales of motion in incompressible turbulent fields at low Reynolds numbers generated by direct numerical simulations. It was observed that although the transfer resulted from triad interactions that were nonlocal in k space, the energy always transferred locally. The energy transfer calculated from the eddy‐damped quasinormal Markovian (EDQNM) theory of turbulence at low Reynolds numbers is in excellent agreement with the results of the numerical simulations. At high Reynolds numbers the EDQNM theory predicts the same transfer mechanism in the inertial range that is observed at low Reynolds numbers, i.e., predominantly local transfer caused by nonlocal triads. The weaker, nonlocal energy transfer is from large to small scales at high Reynolds numbers and from small to large scales at low Reynolds numbers.

An analysis of subgrid‐scale interactions in numerically simulated isotropic turbulence

Using a velocity field obtained in a direct numerical simulation of isotropic turbulence at moderate Reynolds number the subgrid‐scale energy transfer in the spectral and the physical space representation is analyzed. The subgrid‐scale transfer is found to be composed of a forward and an inverse transfer component, both being significant in dynamics of resolved scales. Energy exchanges between the resolved and unresolved scales from the vicinity of the cutoff wave number dominate the subgrid‐scale processes and the energetics of the resolved scales are unaffected by the modes with wave numbers greater than twice the cutoff wave number. Correlations between the subgrid‐scale transfer and the large‐scale properties of the velocity field are investigated.

Effective eddy viscosities in implicit large eddy simulations of turbulent flows

We propose a method for computing effective numerical eddy viscosity acting in dissipative numerical schemes used in monotonically integrated large eddy simulations of turbulence. The method is evaluated on an example of a specific nonoscillatory finite volume scheme MPDATA developed for simulations of geophysical flows.

Energy transfer in numerically simulated wall‐bounded turbulent flows

Using velocity fields obtained in direct numerical simulations of turbulent convection and of turbulent channel flow, the energy transfer process among lateral scales of motion in these low Reynolds number flows is analyzed. In all cases the energy is transferred most effectively between scales of similar size. As a result, the subgrid‐scale energy transfer is caused almost exclusively by interactions between resolved scales and subgrid scales characterized by wave numbers not greater than twice the cutoff wave number. The scale dependence of forward and inverse energy transfers contributing to the total subgrid‐scale eddy viscosity is discussed. The local energy transfer between small scales is strongly affected by the nonlocal interactions characterized by a scale separation greater than a factor of 2 in wave number. However, the direct energy transfer between scales satisfying this condition is one order of magnitude less than the local energy transfer between scales of similar size.

The subgrid-scale estimation model in the physical space representation

The subgrid-scale estimation procedure for large eddy simulations developed previously in the spectral (Fourier) representation is extended to the physical space representation. The procedure provides an estimate of the unfiltered velocity field appearing in the definition of the subgridscale stress tensor and consists of two steps. In the deconvolution step an approximate inversion of the filtering operation is performed. Subsequently, the nonlinear step is used to generate a range of subgrid scales on a mesh two times smaller than the mesh employed for a discretization of the resolved quantities. The modeling procedure is evaluated by comparing results of large eddy simulations of turbulent channel flow with the corresponding results of direct numerical simulations, experiments, and other large eddy simulations.

Direct numerical simulations of passive scalars with Pr > 1 advected by turbulent flow

Direct numerical simulations of passive scalars, with Prandtl numbers Pr =3, 5, and 7, advected by turbulence at three low Reynolds numbers were performed. The energy spectra are self-similar under the Kolmogorov scaling and exhibit behaviour consistent with many other investigations: a short inertial range for the highest Reynolds number and the universal exponential form of the spectrum for all Reynolds numbers in the dissipation range. In all cases the passive scalar spectra collapse to a single self-similar curve under the Batchelor scaling and exhibit the k −1 range followed by an exponential fall-off. We attribute the applicability of the Batchelor scaling to our low-Reynolds-number flows to the universality of the energy dissipation spectra. The Batchelor range is observed for wavenumbers in general agreement with experimental observations but smaller than predicted by the classical estimates. The discrepancy is caused by the fact that the velocity scales responsible for the generation of the Batchelor range are in the vicinity of the wavenumber of the maximum energy dissipation, which is one order of magnitude less than the Kolmogorov wavenumber used in the classical theory. Two different functional forms of passive scalar spectra proposed by Batchelor and Kraichnan were fitted to the simulation results and it was found that the Kraichnan model agrees very well with the data while the Batchelor formula displays systematic deviations from the data. Implications of these differences for the experimental procedures to measure the energy and passive scalar dissipation rates in oceanographic flows are discussed.

Small‐scale properties of nonlinear interactions and subgrid‐scale energy transfer in isotropic turbulence

Using results of direct numerical simulations of isotropic turbulence the subgrid‐scale energy transfer in the physical space is calculated exactly employing a spectral decomposition of the velocity field into large (resolved) and small (unresolved) scales. Comparisons with large‐scale quantities reveal large qualitative correlations between regions of subgrid transfer and the boundaries of regions of large vorticity production. This suggests a novel analysis of the nonlinear term, where it is decomposed into four components determined by four combinations of the resolved and unresolved velocity and vorticity fields. It is found that there is a 90% vector‐correlation between the subgrid transfer and the component of the full transfer associated with the resolved velocity and unresolved vorticity, but that 90% of the total subgrid energy production is determined by the component associated with the unresolved velocity and resolved vorticity. These results suggest subgrid‐scale models that have higher corre...

Direct numerical simulation of transition to turbulence in Görtler flow

Using direct numerical simulation techniques we investigate transition to turbulence in a boundary-layer flow containing two large-scale counter-rotating vortices with axes aligned in the streamwise direction. The vortices are assumed to have been generated by the Gortler instability mechanism operating in boundary-layer flows over concave walls. Full, three-dimensional Navier-Stokes equations in a natural curvilinear coordinate system for a flow over concave wall are solved by a pseudospectral numerical method