Session LD: Turbulence Simulations II

Fully adaptive LES of homogeneous turbulent flows

With the recent development of wavelet-based techniques for computational fluid dynamics, adaptive numerical simulations of turbulent flows have become feasible. Adaptive wavelet methods are based on wavelet threshold filtering that makes it possible to separate coherent energetic eddies, which are numerically resolved, from residual background flow structures that are filtered out. The prescription of a given threshold for wavelet filtering directly links to the desired turbulence resolution. A new original strategy is presented for which the wavelet filtering threshold is not prescribed a-priori but determined on the fly for a given and known level of turbulence resolution. A completely adaptive eddy capturing approach that allows to perform variable fidelity numerical simulations of homogeneous turbulent flows is proposed. The new method is based on wavelet filtering with time-dependent thresholding that automatically adapts to the actual flow conditions in order to achieve the desired level of turbulence resolution. The filtered governing equations supplemented by a localized dynamic energy-based closure model are solved by means of the adaptive wavelet collocation numerical method.   

An hybrid a priori/a posteriori method for assessing LES models

An hybrid approach combining the advantages of a priori and a posteriori methods is proposed for assessing the efficiency of LES models. The LES and the DNS are run simultaneously and an artificial forcing is used to maintain the LES field as close as possible to the filtered DNS field. Various diagnostics on this forcing are used to assess the quality of the LES model.   

A Subgrid Scale Estimation Model for Large Eddy Simulation

We propose a novel estimation procedure to model the subgrid velocity for Large Eddy Simulation (LES). The subgrid stress is obtained directly from the estimated subgrid velocity. The subgrid velocity is modeled as a function of resolved velocity ($\overline{u}_i$) and resolved strain--rate tensor ($\overline {S}_{ij}$). Using tensor invariants, we obtain an expression for subgrid velocity that is linear in $\overline{u}_i$ and quadratic in $\overline{S}_{ij}$ with three undetermined coefficients. These three coefficients are obtained by imposing the following constraints: (i)Galilean invariance, (ii)ensemble- averaged subgrid dissipation and (iii)local subgrid kinetic energy. The subgrid dissipation may be obtained through either eddy--viscosity models or a new dynamic model for dissipation. The subgrid kinetic energy may be obtained either from the dynamic Yoshizawa model or a modeled transport equation. The estimation model is applied to isotropic turbulence and good results are obtained. Realistic backscatter is also predicted. We also extend the estimation procedure to LES of passive scalar transport and propose an estimation model for subgrid scale scalar concentration. The model is applied to decaying isotropic turbulence with an uniform mean scalar gradient and good results are obtained.   

Quantification of Sub-Grid-Scale Terms in Plasma Turbulence

The notions of DNS and LES are well established in hydrodynamic turbulence. We apply similar ideas to plasma turbulence whose governing equation (i.e., the Vlasov or Fokker-Planck equation) is higher dimensional (generally 6D). Analogously to the Navier-Stokes LES equations, we filter and derive sub-grid-scale terms for the Vlasov equation. It is known in gyrokinetic plasma turbulence that nonlinear interactions in velocity space lead small scales generation of the distribution function up to the collisional scales (see Schekochihin et al., Plasma Phys. Control. Fusion 2008). Because the gyrokinetic description still requires a 5D phase space description, and hence is computationally expensive, our first approach is to quantify the SGS terms in the context of drift kinetic equations in 4D phase space under the electrostatic approximation using high resolutions of up to a billion grid cells. We examine the phenomenology of the SGS terms by a careful quantification using high-order DNS of drift kinetic turbulence. The eventual goal is to develop SGS models for use in under-resolved or LES of plasma turbulence.   

Dynamic Lagrangian model and wall model for LES on unstructured grids

We discuss a dynamic Lagrangian averaging approach applied in conjunction with the standard dynamic model for large-eddy simulation. Unlike the conventional Lagrangian dynamic model where the Lagrangian time scale contains an adjustable parameter $\theta$, we propose a dynamic time scale based on a ``surrogate-correlation'' of the Germano-identity error. The absence of any multi-linear interpolation makes this approach particularly suitable for unstructured grids. We also discuss a dynamic wall model obtained by incorporating RANS constraints into a dynamic SGS model. Unlike conventional approaches, Reynolds stresses are used as constraints on the mean SGS stress so that the constraining Reynolds stress closely matches the computed stress only in the mean sense. We use the Germano-identity error as an indicator of LES quality so that the RANS constraints are activated only where the Germano-identity error exceeds a certain threshold. These proposed models are applied to LES of turbulent channel flow at various Reynolds numbers and grid resolutions to obtain significant improvement over the dynamic Smagorinsky model, especially at coarse resolutions.   

Assessment of SGS models in an $Re_{\tau}=2000$ channel flow

Typical validation of subgrid scale models for large-eddy simulation are performed at a relatively low Reynolds numbers and at reasonably fine resolutions. We assess the performance of subgrid scale models for large-eddy simulation at a high Reynolds number. Explicitly filtered large-eddy simulations of a fixed pressure gradient driven $Re_{\tau}=2000$ channel flow are performed using the dynamic Smagorinsky, dynamic Vreman (You \& Moin, 2007; Vreman, 2004), and a dynamic eddy viscosity model with $\nu_t = Ck_{sgs}|\bar{S}|^{-1}$. The resolution of LES simulations is chosen to be quite coarse ($\Delta x^+_f \approx 155$, $\Delta z^+_f \approx 78$) in order to highlight the deficiencies of the subgrid scale models. Mean velocity profiles, rms fluctuations, and one dimensional energy spectra are compared with both filtered DNS and unfiltered DNS (Hoyas \& Jimenez, 2006). The $k_{sgs}|\bar{S}|^{-1}$ model most accurately predicts the mean velocity profile, predicts the mass flux within 1.5\%, and the centerline velocity within 3\%. The effect of using a global coefficient for the eddy viscosity model versus a wall normal varying model coefficient will also be discussed.   

A new dynamic eddy viscosity model for LES

A new dynamic eddy viscosity model based on the geometric mean of the eigenvalues of the resolved strain rate tensor, $\nu_t \sim \Delta^2 (\lambda_1 \lambda_2 \lambda_3)^{1/3}$, is proposed. The model is derived from the formal construction of the minimal eddy viscosity that is required to guarantee that all scales smaller than the filter width, $\Delta$, are dissipated. This dynamic eddy viscosity model correctly predicts the decay rate for decaying isotropic turbulence and the predicted energy spectra are in good agreement with filtered DNS results. The mean velocity profile and the rms fluctuations are also in good agreement with filtered DNS results in an $Re_{\tau} = 590$ channel flow using this model. It is shown that the eddy viscosity also obeys a $y^3$ scaling near the wall when the model coefficient is computed using the dynamic procedure of Germano \emph{et al.} (1991). The eddy viscosity properly vanishes for laminar flows and at solid boundaries, even without the aid of the dynamic procedure.   

On the physics of turbulent flows in natural meander bends: Insights gained by LES

Turbulent flow in a natural meander bend with riffle-pool sequences and arbitrarily complex large-scale roughness elements is simulated using high-resolution LES. The complex stream bathymetry is handled with a new version of the curvilinear immersed boundary method capable of carrying out LES in arbitrarily complex geometries with the dynamic Smagorinsky model and wall modeling. The computational grid is sufficiently fine to resolve vortex shedding from cm-scale roughness elements in the riffles. The computed results are compared with experimental data and are shown to be in good overall agreement. The simulated flowfields are analyzed to provide new insights into the structure and driving mechanisms of the inner and outer bank secondary flow cells, the effects of large-scale roughness on turbulence anisotropy and anisotropy-driven secondary flows in the riffles, and the structure and impact of recirculation regions along the inner bank of the bend. The simulated flowfields also underscore and clarify previously hypothesized linkages between flow patterns and experimentally documented streambed morphodynamics.