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

In his pioneering work Lighthill formulated the problem of predicting the noise radiated by an unsteady flow in terms of an acoustic analogy. However, in order to predict the far-field noise the acoustic source terms of such acoustic analogies must be known accurately. Such detailed information is usually not available and empirical models of the acoustic sources are utilized to arrive at an empirical prediction of the far-field noise. Recent advances in direct and large eddy simulations of turbulent flows provide an alternative to this empiricism. The far-field noise can be obtained from first principles by using the ‘exact’ source terms from DNS/LES in an acoustic analogy. Developing the methods to make this possible and studying the nature of particular flow processes responsible for the most intense noise are the principal objectives of the research underway at Stanford.

Direct Computation of Aerodynamic Noise

/pdf/transitional-and-turbulent-flat-plate-boundary-layers-with-3im78bec8m.pdf

Transitional and turbulent flat-plate boundary layers with heat transfer

Large Eddy Simulation of a Swirling Confined Coaxial Jet

In the limit of increasingly large Reynolds numbers, the feasibility of direct numerical simulations (DNS) of the Navier-Stokes equations becomes impractical. A widely used tool aimed at alleviating this issue is the large-eddy simulation (LES) methodology, wherein the simulations are coarse-grained relative to a DNS. The large eddies in the flow are resolved numerically, but the unresolved eddies are modeled using physics-inspired phenomenological models (Smagorinsky 1963; Germano et al. 1991; Nicoud et al. 2011; Vreman et al. 1994). A commonly utilized framework for subgrid-scale (SGS) modeling is the eddy-viscosity formulation using both static (Smagorinsky 1963; Vreman 2004; Rozema et al. 2015) and dynamic methods (Germano et al. 1991; Ghosal et al. 1995; Meneveau et al. 1996). The dynamic procedure (based on the idea of test filtering) was introduced to alleviate the ad hoc prescription of a model coefficient to the numerous SGS models depending on the flow. However, in all of these formulations, the SGS stresses are assumed to be locally aligned and scaled with the strain rates of the resolved eddies, thus acting as a further diffusive source of momentum in addition to the molecular viscosity. Recently, Agrawal et al. (2022) showed that in both a-priori and a-posteriori calculations, a non-Boussinesq formulation of the SGS stresses, or the dynamic tensor-coefficient Smagorinsky model (DTCSM), outperforms the classical eddy-viscosity models. For wall-bounded turbulence, as the Reynolds number increases, the size of the largest energy-containing eddies in the outer part of the boundary layer becomes increasingly large compared to the near-wall eddies. This means that significant grid refinement close to the wall is required to accurately resolve the near-wall eddies, even within the LES paradigm. Choi & Moin (2012) suggest that the grid requirements for such calculations scale with a super-linear power of the Reynolds number, thus making the numerical simulations expensive. To reduce the issues related to this intractability, the effect of the subgrid, near-wall flow within the turbulent boundary layer is modeled, and this method is referred as wall-modeled LES (WMLES). Traditionally, wall-modeling practices include wall-stress models which supply a flux (or wall stress) to the outer LES solution in the form of a boundary condition. These wall models are principally motivated by the Reynolds-averaged Navier-Stokes (RANS) form of the thin-boundary-layer equations (see Bose & Park (2018) for more details). One of the most commonly used wall models is the equilibrium wall model (EQWM), in which the near-wall eddies are assumed to be in local equilibrium. In this framework, a non-zero flux is supplied to the outer LES in the streamwise and spanwise directions, with the non-penetrating Dirichlet boundary condition. This model has been successfully applied in both canonical flows (Kawai & Larsson 2012; Lozano-Durán & Bae 2019) and

Wall-modeled LES of the Boeing speed bump using a non-Boussinesq modeling framework

A method of constructing discrete filters for large eddy simulation of turbulent flows on unstructured meshes is presented. The commutation error between differentiation and filtering can be made arbitrarily small with these filters. The filtering method is applied to various test cases to demonstrate commutation. An extension to three dimensions and implementation into an unstructured solver for LES are discussed.

Parviz Moin

Papers

Direct Computation of Aerodynamic Noise

Transitional and turbulent flat-plate boundary layers with heat transfer

Large Eddy Simulation of a Swirling Confined Coaxial Jet

Wall-modeled LES of the Boeing speed bump using a non-Boussinesq modeling framework

Construction of Commutative Filters for LES on Unstructured Meshes