##### Document Text Contents

Page 57

and the constant in the eddy diffusivity equation can be taken as cT = 0.15,

similar in magnitude to the Smagorinsky model in velocity variables, then

the evolution equation for vorticity is

Dωi

Dt

= ω · ∇ui + ν∇2ωi + νT

(

∂ωi

∂xj∂xj

− ∂ωj

∂xi∂xj

)

. (3.15)

The authors also mention the following.

Note that Φij represents subgrid-scale vortex stretching and tilt-

ing due to unresolved motion, while Φji reflects vortex transport

by subgrid-scale velocity fluctuations.

Mansfield et al [238], proposes a dynamic eddy-diffusivity LES model in

the vorticity variables based on two-level filtering of the vorticity field and

compares vortex methods to spectral methods in a simulation of homogenous

isotropic turbulence. The scheme uses an eddy diffusivity model that, by

construction, creates no subfilter torque.

More applicable is Cottet [281], which introduces a Lagrangian method for

LES consisting of an anisotropic and less-diffusive method. The work lever-

ages the truncation error normally produced by unremeshed vortex methods.

Using the vorticity formulation of the Navier-Stokes equations, Cottet et al

[282] describe two new LES formulations, one based on the vorticity angles.

Vortex methods are not used?

Gharakhani [274] presents an application of the vorticity redistribution

method [248] for large-eddy simulation.

Milane [257] uses a diffusion velocity method to compute LES solutions

in a 2D mixing layer.

A large question remains: how does one accommodate the subgrid-scale

modeling of a sheet of discontinuity? It is even possible? Lundgren et al

[283] make an interesting observation:

The roll-up of unstable Helmholtz vorticies [has] effectively pro-

duced a thicker interface... It is our point of view that by com-

puting with larger [values for Krasny’s] δ we simulate the effect

of averaging over these ‘turbulent’ fluctuations.

56

and the constant in the eddy diffusivity equation can be taken as cT = 0.15,

similar in magnitude to the Smagorinsky model in velocity variables, then

the evolution equation for vorticity is

Dωi

Dt

= ω · ∇ui + ν∇2ωi + νT

(

∂ωi

∂xj∂xj

− ∂ωj

∂xi∂xj

)

. (3.15)

The authors also mention the following.

Note that Φij represents subgrid-scale vortex stretching and tilt-

ing due to unresolved motion, while Φji reflects vortex transport

by subgrid-scale velocity fluctuations.

Mansfield et al [238], proposes a dynamic eddy-diffusivity LES model in

the vorticity variables based on two-level filtering of the vorticity field and

compares vortex methods to spectral methods in a simulation of homogenous

isotropic turbulence. The scheme uses an eddy diffusivity model that, by

construction, creates no subfilter torque.

More applicable is Cottet [281], which introduces a Lagrangian method for

LES consisting of an anisotropic and less-diffusive method. The work lever-

ages the truncation error normally produced by unremeshed vortex methods.

Using the vorticity formulation of the Navier-Stokes equations, Cottet et al

[282] describe two new LES formulations, one based on the vorticity angles.

Vortex methods are not used?

Gharakhani [274] presents an application of the vorticity redistribution

method [248] for large-eddy simulation.

Milane [257] uses a diffusion velocity method to compute LES solutions

in a 2D mixing layer.

A large question remains: how does one accommodate the subgrid-scale

modeling of a sheet of discontinuity? It is even possible? Lundgren et al

[283] make an interesting observation:

The roll-up of unstable Helmholtz vorticies [has] effectively pro-

duced a thicker interface... It is our point of view that by com-

puting with larger [values for Krasny’s] δ we simulate the effect

of averaging over these ‘turbulent’ fluctuations.

56