We formulate a subgrid eddy viscosity method for solving the steady-state incompressible flow problem. The eddy viscosity does not act on the large flow structures. Optimal error estimates are obtained for velocity and pressure. The numerical illustrations agree completely with the theoretical expectations.

An eddy-viscosity based, subgrid-scale model for Large Eddy Simulations is derived from the analysis of the singular values of the resolved velocity gradient tensor. It is shown that the proposed σ-model has the property to automatically vanish as soon as the resolved field is two-dimensional, including the pure shear and solid rotation cases. In addition, the model generates no subgrid-scale v...

This paper presents a stability, convergence and error analysis for two modular, projection-based variational multiscale (VMS) methods for the incompressible Naiver-Stokes equations. In VMS methods, the influence of the unresolved scales onto the resolved small scales is modeled by a Smagorinsky-type turbulent viscosity acting only on the marginally resolved scales. We analyze a method of induc...

The variational multiscale method is applied to the large eddy simulation ~LES! of homogeneous, isotropic flows and compared with the classical Smagorinsky model, the dynamic Smagorinsky model, and direct numerical simulation ~DNS! data. Overall, the multiscale method is in better agreement with the DNS data than both the Smagorinsky model and the dynamic Smagorinsky model. The results are some...

In order to gain insight into the one-dimensional turbulence (ODT) model of Kerstein [1] as it pertains to residual stress closure in large-eddy simulation (LES), we develop ensemble mean closure (EMC), an algebraic stress closure based on the mappings and time scale physics employed in ODT. To allow analytic determination of the stress the ODT model is simplified, conceptually, such that eddy ...

It is shown that a new mixed nonlinear/eddy viscosity LES model reproduces profiles better than a number of competing nonlinear and mixed models for plane channel flow. The objective is an LES method that produces a fully resolved turbulent boundary layer and could be applied to a variety of aerospace problems that are currently studied with RANS, RANS-LES, or DES methods that lack a true turbu...

Large-eddy simulation of particle-laden turbulent channel flow is investigated for several subgrid models and Stokes numbers with the objective to investigate the accuracy of the subgrid models studied with respect to particle behavior. It is shown that the wall-normal particle velocity and particle velocity fluctuations are reduced compared to DNS, if the filtered fluid velocity calculated in ...

A new Boussinesq-type model describing periodic wave propagation over a constant depth has been developed for the cases where the effects of a turbulent boundary layer are significant. In this paper, the eddy viscosity model is employed in the turbulent boundary layer and is further approximated as a linear function of the distance measured from the seafloor. The boundary-layer velocities are c...

Abstract. We present and analyze a subgrid viscosity Lagrange-Galerkin method that combines the subgrid eddy viscosity method proposed in W. Layton, A connection between subgrid scale eddy viscosity and mixed methods. Appl. Math. Comp., 133: 147-157, 2002, and a conventional Lagrange-Galerkin method in the framework of P1⊕ cubic bubble finite elements. This results in an efficient and easy to i...

Solving Navier-Stokes equations using monotone algorithms often produces results that are consistent with the dynamics of high Reynolds number turbulence despite formally insufficient numerical resolution to capture all physically relevant scales of motion. It is frequently argued that the truncation error of a numerical scheme provides a mechanism for the energy dissipation and serves as an im...