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

TitleSummary of Vortex Methods Literature (A living - Mark J. Stock
LanguageEnglish
File Size723.1 KB
Total Pages115
Table of Contents
                            Introduction
	Advantage of vorticity variables
	Advantage of Lagrangian methods
		Front-tracking vs. front-capturing
	Advantages of vortex methods
	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
		Core-spreading techniques
		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
	Particle-laden flows
	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.

56

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