# Download Summary of Vortex Methods Literature (A living - Mark J. Stock PDF

Title Summary of Vortex Methods Literature (A living - Mark J. Stock English 723.1 KB 115
```                            Introduction
Front-tracking vs. front-capturing
Other Lagrangian methods
Velocity Field Calculation
Discretization of vorticity
Vortex particle methods
Vortex filament methods
Vortex sheet methods
Vortex volume methods
Level Set method
Magnet/impulse elements
Semi-Lagrangian particles
Pure Eulerian
Combinations
Solution methods for the Biot-Savart equation
Direct integration
Vortex-In-Cell (VIC)
Treecode/Fast Multipole Method (FMM)
Other methods
Corrections due to boundaries
Domain boundaries
Internal boundaries
Fluid-structure interaction
Other topics
Time integration and discretization
Particle-grid operators
Domain decomposition
Vorticity divergence
Computing derivatives
Generalized Helmholtz decomposition
Diagnostics/Conserved quantities
Forces on bodies
The Vorticity Equation
Vortex stretching
Particle discretization
Filament discretization
Sheet discretization
Diffusion methods
Random walk
Hairpin removal
Particle Strength Exchange (PSE)
Vorticity Redistribution Method (VRM)
Free-Lagrangian method
Eulerian formulations
Other methods
Large Eddy Simulation (LES)
Vorticity creation at walls
Euler limit
Viscous
Baroclinic generation
Weak stratification
Strong stratification
Surface tension
Rotating frame
Transport Elements/Scalar Transport Equation
Front-Tracking
Scalar field definition and reconstruction
Transport element method
Local Integral Moment (LIM)
Level Set
Combustion
Fractal representation
Compressibility Effects
Aerodynamic Sound
Co-location with source particles
Sample Simulations
Free-boundary, homogenous flows
Multifluid flows
Flows with solid boundaries
Compressible flows
Closing remarks
```
##### 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.

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