Energy transfers and spectral eddy viscosity in large-eddy simulations of homogeneous isotropic turbulence: Comparison of dynamic Smagorinsky and multiscale models over a range of discretizations

Abstract

Energy transfers within large-eddy simulation (LES) and direct numerical simulation (DNS) grids are studied. The spectral eddy viscosity for conventional dynamic Smagorinsky and variational multiscale LES methods are compared with DNS results. Both models underestimate the DNS results for a very coarse LES, but the dynamic Smagorinsky model is significantly better. For moderately to well-refined LES, the dynamic Smagorinsky model overestimates the spectral eddy viscosity at low wave numbers. The multiscale model is in good agreement with DNS for these cases. The convergence of the multiscale model to the DNS with grid refinement is more rapid than for the dynamic Smagorinsky model.

YZβ discontinuity capturing for advection‐dominated processes with application to arterial drug delivery

“…[29][30][31]), founded on the variational multiscale formulation of the Navier-Stokes equations of incompressible flows (see e.g. [32][33][34][35][36][37]), is used for the fluid mechanics part. These residual-based methods possess a dual nature: on the one hand, they are bona-fide LES-like turbulence models, and on the other hand, they may be thought of as stabilized methods, such as the SUPG formulation, extended to the nonlinear realm and capable of accurately solving laminar flows.…”

Weak Dirichlet boundary conditions for wall-bounded turbulent flows

“…Variational equation (17) differs from (8) only in the last term on the left-hand side, and it may be thought of as a generalization of (8). Selecting y to be a constant multiple of the wall-normal mesh size h b , that is, y = h b /C I b , and letting h b go to zero, the Spalding equation (14a) reduces to y + = u + , which is a well-known parameterization of the viscous sublayer.…”

“…[1,6,15]), which is based on the Variational Multiscale Formulation (see e.g. [10][11][12][13][14]17]). These residual-based methods possess a dual nature: on the one hand they are bona-fide LES-like turbulence models, and on the other hand they may be thought of as stabilized methods, such as SUPG [5], extended to the nonlinear realm.…”

Simulations of the turbulent channel flow at Reτ = 180 with projection‐based finite element variational multiscale methods

“…However, in our opinion, a potential advantage of the VMS approach is that simple models for the influence of the unresolved scales can be applied since these models act directly only on a part of the resolved scales and the importance of the model is reduced in this way. A constant Smagorinsky model was used in the first numerical simulations of turbulent flows with VMS methods [14,15] and a dynamic model, for instance, in [45] (without comparison to the constant Smagorinsky model) and in [17]. In [17], it was shown that the constant Smagorinsky model within the VMS methods led to highly accurate results for appropriate scale separations (in terms of wave numbers of a Fourier spectral method) but the dynamic model was less sensitive to the chosen scale partition.…”