A New Mesh-Free Vortex Method
Shankar Subramaniam
To:
Abstract
A New Mesh-Free Vortex Method
Shankar Subramaniam
August 12, 1996
To my family.
Abstract
1
. Introduction
1
.
1
The need for mesh-free Lagrangian methods
1
.
2
Hybrid methods for diffusion
1
.
3
Lagrangian methods for diffusion
1
.
3
.
1
Random walk method
1
.
3
.
2
Core expansion method
1
.
3
.
3
Deterministic particle method
1
.
3
.
4
Fishelov's method
1
.
3
.
5
Diffusion velocity method
1
.
3
.
6
Free-Lagrange method
1
.
4
The vorticity redistribution method
1
.
5
Organization of the thesis
2
. Governing Equations
2
.
1
Navier-Stokes equations
2
.
2
Velocity field
2
.
3
Vorticity conservation laws
2
.
4
Summary
3
. Vortex Methods
3
.
1
Vortex methods for inviscid flows
3
.
2
Vortex methods for viscous flows
3
.
3
Summary
4
. Vorticity Redistribution Method
4
.
1
Mathematical formulation
4
.
2
Physical meaning of the equations
4
.
3
General justification
4
.
4
Summary
5
. Convergence Analysis
6
. Numerical Implementation
6
.
1
Numerical implementation of convection
6
.
2
Numerical implementation of diffusion
6
.
2
.
1
Finding the redistribution amounts
6
.
2
.
2
Least maximum solution procedure
6
.
2
.
3
Adding vortices
6
.
2
.
4
Merging vortices
6
.
2
.
5
Cut-off circulation
6
.
2
.
6
Evaluation of the vorticity
6
.
3
Boundary condition
6
.
4
Summary
7
. Computation of Flows in Free Space
7
.
1
Point vortex
7
.
1
.
1
Governing equations
7
.
1
.
2
Vorticity field
7
.
2
Counter-rotating vortex pair
7
.
2
.
1
Governing equations
7
.
2
.
2
Vorticity field
7
.
2
.
3
Drift velocity
7
.
2
.
4
Summary
7
.
3
Three-dimensional Stokes flows
8
. Computation of Flows over Solid Walls
8
.
1
Impulsively rotated cylinder
8
.
2
Impulsively translated cylinder
8
.
2
.
1
Review of previous computations
8
.
2
.
2
Streamlines
8
.
2
.
3
Velocity field
8
.
2
.
4
Vorticity field
8
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2
.
5
Drag force
8
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2
.
6
Effects of cut-off circulation
8
.
2
.
7
Comparison with boundary layer theory
8
.
2
.
8
The drag near the Van Dommelen & Shen time
8
.
2
.
9
Performance compared with previous methods
8
.
2
.
10
Summary
8
.
3
Vortex-pair/cylinder interaction
8
.
4
Summary
9
. Discussion
9
.
1
Resolution of short scales
9
.
2
Automatic remeshing
9
.
3
Computational speed
9
.
4
Simplicity
9
.
5
Conservation laws and positivity
10
. Conclusions
A. Detailed derivations
Bibliography
Acknowledgements
Biographical Sketch
List of Tables
List of Figures
Contents
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Abstract
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