We study the construction of subgrid-scale models for large-eddy simulation of incompressible turbulent flows. In particular, we aim to consolidate a systematic approach of constructing subgrid-scale models, based on the idea that it is desirable that subgrid-scale models are consistent with the mathematical and physical properties of the Navier-Stokes equations and the turbulent stresses.To that end, we first discuss in detail the symmetries of the Navier-Stokes equations, and the near-wall scaling behavior, realizability and dissipation properties of the turbulent stresses. We furthermore summarize the requirements that subgrid-scale models have to satisfy in order to preserve these important mathematical and physical properties. In this fashion, a framework of model constraints arises that we apply to analyze the behavior of a number of existing subgrid-scale models that are based on the local velocity gradient. We show that these subgrid-scale models do not satisfy all the desired properties, after which we explain that this is partly due to incompatibilities between model constraints and limitations of velocity-gradient-based subgrid-scale models. However, we also reason that the current framework shows that there is room for improvement in the properties and, hence, the behavior of existing subgrid-scale models. We furthermore show how compatible model constraints can be combined to construct new subgrid-scale models that have desirable properties built into them. We provide a few examples of such new models, of which a new model of eddy viscosity type, that is based on the vortex stretching magnitude, is successfully tested in large-eddy simulations of decaying homogeneous isotropic turbulence and turbulent plane-channel flow.

Direct numerical simulations of the incompressible Navier-Stokes equations are not feasible yet for most practical turbulent flows. Therefore, dynamically less complex mathematical formulations are necessary for coarse-grained simulations. In this regard, eddy-viscosity models for Large-Eddy Simulation (LES) are probably the most popular example thereof. This type of models requires the calculation of a subgrid characteristic length which is usually associated with the local grid size. For isotropic grids this is equal to the mesh step. However, for anisotropic or unstructured grids, such as the pancake-like meshes that are often used to resolve near-wall turbulence or shear layers, a consensus on defining the subgrid characteristic length has not been reached yet despite the fact that it can strongly affect the performance of LES models. In this context, a new definition of the subgrid characteristic length is presented in this work. This flow-dependent length scale is based on the turbulent, or subgrid stress, tensor and its representations on different grids. The simplicity and mathematical properties suggest that it can be a robust definition that minimizes the effects of mesh anisotropies on simulation results. The performance of the proposed subgrid characteristic length is successfully tested for decaying isotropic turbulence and a turbulent channel flow using artificially refined grids. Finally, a simple extension of the method for unstructured meshes is proposed and tested for a turbulent flow around a square cylinder. Comparisons with existing subgrid characteristic length scales show that the proposed definition is much more robust with respect to mesh anisotropies and has a great potential to be used in complex geometries where highly skewed (unstructured) meshes are present. *

Using a symmetry adapted polaron transformation of the Holstein Hamiltonian, we study the interplay of electronic excitation-vibration couplings, resonance excitation transfer interactions, and temperature in the linear absorption spectra of molecular J-aggregates. Semi-analytical expressions for the spectra are derived and compared with results obtained from direct numerical diagonalization of the Hamiltonian in the two-particle basis set representation. At zero temperature, we show that our polaron transformation reproduces both the collective (exciton) and single-molecule (vibrational) optical response associated with the appropriate standard perturbation limits. Specifically, for the molecular dimer excellent agreement with the spectra from the two-particle approach for the entire range of model parameters is obtained. This is in marked contrast to commonly used polaron transformations. Upon increasing the temperature, the spectra show a transition from the collective to the individual molecular features, which results from the thermal destruction of the exciton coherence.

Assuming a general constitutive relation for the turbulent stresses in terms of the local large-scale velocity gradient, we constructed a class of subgrid-scale models for large-eddy simulation that are consistent with important physical and mathematical properties. In particular, they preserve symmetries of the Navier-Stokes equations and exhibit the proper near-wall scaling. They furthermore show desirable dissipation behavior and are capable of describing nondissipative effects. We provided examples of such physically-consistent models and showed that existing subgrid-scale models do not all satisfy the desired properties.

Predicting the behavior of turbulent flows using large-eddy simulation requires a modeling of the subgrid-scale stress tensor. This tensor can be approximated using mixed models, which combine the dissipative nature of functional models with the capability of structural models to approximate out-of-equilibrium effects. We propose a mathematical basis to mix (functional) eddy-viscosity models with the (structural) Bardina model. By taking an anisotropic minimum-dissipation (AMD) model for the eddy viscosity, we obtain the (single-layer) AMD–Bardina model. In order to also obtain a physics-conforming model for wall-bounded flows, we further develop this mixed model into a two-layer approach: the near-wall region is parameterized with the AMD–Bardina model, whereas the outer region is computed with the Bardina model. The single-layer and two-layer AMD–Bardina models are tested in turbulent channel flows at various Reynolds numbers, and improved predictions are obtained when the mixed models are applied in comparison to the computations with the AMD and Bardina models alone. The results obtained with the two-layer AMD–Bardina model are particularly remarkable: both first- and second-order statistics are extremely well predicted and even the inflection of the mean velocity in the channel center is captured. Hence, a very promising model is obtained for large-eddy simulations of wall-bounded turbulent flows at moderate and high Reynolds numbers.