One major drawback of the eddy viscosity subgrid‐scale stress models used in large‐eddy simulations is their inability to represent correctly with a single universal constant different turbulent fields in rotating or sheared flows, near solid walls, or in transitional regimes. In the present work a new eddy viscosity model is presented which alleviates many of these drawbacks. The model coefficient is computed dynamically as the calculation progresses rather than input a priori. The model is based on an algebraic identity between the subgrid‐scale stresses at two different filtered levels and the resolved turbulent stresses. The subgrid‐scale stresses obtained using the proposed model vanish in laminar flow and at a solid boundary, and have the correct asymptotic behavior in the near‐wall region of a turbulent boundary layer. The results of large‐eddy simulations of transitional and turbulent channel flow that use the proposed model are in good agreement with the direct simulation data.

A dynamic subgrid‐scale eddy viscosity model

We present an overview of the lattice Boltzmann method (LBM), a parallel and efficient algorithm for simulating single-phase and multiphase fluid flows and for incorporating additional physical complexities. The LBM is especially useful for modeling complicated boundary conditions and multiphase interfaces. Recent extensions of this method are described, including simulations of fluid turbulence, suspension flows, and reaction diffusion systems.

Lattice boltzmann method for fluid flows

Considerable confusion surrounds the longstanding question of what constitutes a vortex, especially in a turbulent flow. This question, frequently misunderstood as academic, has recently acquired particular significance since coherent structures (CS) in turbulent flows are now commonly regarded as vortices. An objective definition of a vortex should permit the use of vortex dynamics concepts to educe CS, to explain formation and evolutionary dynamics of CS, to explore the role of CS in turbulence phenomena, and to develop viable turbulence models and control strategies for turbulence phenomena. We propose a definition of a vortex in an incompressible flow in terms of the eigenvalues of the symmetric tensor ${\bm {\cal S}}^2 + {\bm \Omega}^2$ are respectively the symmetric and antisymmetric parts of the velocity gradient tensor ${\bm \Delta}{\bm u}$. This definition captures the pressure minimum in a plane perpendicular to the vortex axis at high Reynolds numbers, and also accurately defines vortex cores at low Reynolds numbers, unlike a pressure-minimum criterion. We compare our definition with prior schemes/definitions using exact and numerical solutions of the Euler and Navier–Stokes equations for a variety of laminar and turbulent flows. In contrast to definitions based on the positive second invariant of ${\bm \Delta}{\bm u}$ or the complex eigenvalues of ${\bm \Delta}{\bm u}$, our definition accurately identifies the vortex core in flows where the vortex geometry is intuitively clear.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112095000462

On the identification of a vortex

http://home.eps.hw.ac.uk/~ab226/tmp/implicit/lele_92.pdf

Compact finite difference schemes with spectral-like resolution

/pdf/turbulence-and-the-dynamics-of-coherent-structures-i-1o6o6m60fm.pdf

Turbulence and the dynamics of coherent structures. I. Coherent structures

We present a numerical formulation for the treatment of nonlinear instabilities in shock-free compressible turbulence simulations. The formulation is high order and contains no artificial dissipation. Numerical stability is enhanced through semi-discrete satisfaction of global conservation properties stemming from the second law of thermodynamics and the entropy equation. The numerical implementation is achieved using a conservative skew-symmetric splitting of the nonlinear terms. The robustness of the method is demonstrated by performing unresolved numerical simulations and large eddy simulations of compressible isotropic turbulence at a very high Reynolds number. Results show the scheme is capable of capturing the statistical equilibrium of low Mach number compressible turbulent fluctuations at infinite Reynolds number. Comparisons with the entropy splitting technique [J. Comput. Phys. 162 (2000) 33; J. Comput. Phys. 178 (2002) 307], staggered method [J. Comput. Phys. 191(2) (2003) 392], and skew-symmetric like schemes [J. Comput. Phys. 161 (2000) 114] confirm the superiority of the current approach. We also discuss a flaw in the skew-symmetric splitting implemented in the literature. Very good results are obtained based on the proper splitting.

Higher entropy conservation and numerical stability of compressible turbulence simulations.

Direct numerical simulation and inviscid linear analysis are used to study the interaction of a normal shock wave with an isotropic turbulent field of vorticity and entropy fluctuations. The role of the upstream entropy fluctuations is emphasized. The upstream correlation between the vorticity and entropy fluctuations is shown to strongly influence the evolution of the turbulence across the shock. Negative upstream correlation between u′ and T′ is seen to enhance the amplification of the turbulence kinetic energy, vorticity and thermodynamic fluctuations across the shock wave. Positive upstream correlation has a suppressing effect. An explanation based on the relative effects of bulk compression and baroclinic torque is proposed, and a scaling law is derived for the evolution of vorticity fluctuations across the shock. The validity of Morkovin's hypothesis across a shock wave is examined. Linear analysis is used to suggest that shock-front oscillation would invalidate the relation between urms and Trms, as expressed by the hypothesis.

The influence of entropy fluctuations on the interaction of turbulence with a shock wave

The far-field sound from corotating vortices is computed by direct computation of the unsteady, compressible Navier-Stokes equations on a computational mesh that extends to two acoustic wavelengths in all directions. The vortices undergo a period of corotation followed by a sudden merger. A 2D version of Moehring's equation is developed and used in conjunction with source terms computed in the simulation to predict the far-field sound. The prediction agrees with the simulation to within 3 percent. Results of far-field pressure fluctuations for an acoustically noncompact case are also presented for which the prediction is 66 percent too high. Results also indicate that the monopole contribution of 'viscous sound' is negligible for this flow.

Direct computation of the sound from a compressible co-rotating vortex pair

An improvement of the dynamic procedure of Park et al. [Phys. Fluids 18, 125109 (2006)] for closure of the subgrid-scale eddy-viscosity model developed by Vreman [Phys. Fluids 16, 3670 (2004)] is proposed. The model coefficient which is globally constant in space but varies in time is dynamically determined assuming the “global equilibrium” between the subgrid-scale dissipation and the viscous dissipation of which utilization was proposed by Park et al. Like the Vreman model with a fixed coefficient and the dynamic-coefficient model of Park et al., the present model predicts zero eddy-viscosity in regions where the vanishing eddy viscosity is theoretically expected. The present dynamic model is especially suitable for large-eddy simulation in complex geometries since it does not require any ad hoc spatial and temporal averaging or clipping of the model coefficient for numerical stabilization and more importantly, requires only a single-level test filter in contrast to the dynamic model of Park et al., whi...

A dynamic global-coefficient subgrid-scale eddy-viscosity model for large-eddy simulation in complex geometries

The dynamic localization model is a recently developed method that allows one to compute rather than prescribe the unknown coefficients in a subgrid scale model as a function of position at each time‐step. A realistic subgrid scale model should describe both the direct and reverse (backscatter) energy transfers at the local level. A previously developed dynamic localization model accounted for backscatter by means of a (deterministic) eddy viscosity that could locally assume positive as well as negative values. Here this paper presents an alternative stochastic model of backscatter in the context of the dynamic procedure. A comparative discussion of the merits of stochastic versus deterministic modeling of backscatter is presented. These models are applied to a large eddy simulation of isotropic decaying and forced turbulence. Tests are also performed with versions of the model that do not account for backscatter. The results are compared to experiments and direct numerical simulation. It is shown that th...

Parviz Moin

Papers

Higher entropy conservation and numerical stability of compressible turbulence simulations.

The influence of entropy fluctuations on the interaction of turbulence with a shock wave

Direct computation of the sound from a compressible co-rotating vortex pair

A dynamic global-coefficient subgrid-scale eddy-viscosity model for large-eddy simulation in complex geometries

On the representation of backscatter in dynamic localization models