| A New Mesh-Free Vortex Method |
|
Shankar Subramaniam |
|
In chapter 2 we review the governing flow equations and vorticity conservation
laws. In chapter 3 we describe vortex methods in general.
In chapter 4 we formulate our new `vorticity redistribution method'.
In chapter 5 we establish the convergence of the vorticity redistribution
method for the Stokes equations.
In chapter 6 we describe the numerical implementation of the
vorticity redistribution method.
In chapter 7 we apply the method to
flows in free space. We first compute the flow due to the
the decay of point vortices in two-dimensional free space and then
compute two Stokes flows in three-dimensional free space.
In chapter 8 we apply the method to compute
two-dimensional flows over solid walls. We first apply the
method to compute axisymmetric flows over circular cylinders.
Next, we compute the more complicated case of an impulsively translated
circular cylinder for a wide range of Reynolds numbers.
We present the streamlines, velocity fields, vorticity fields,
and the drag coefficients.
We validate our results against boundary layer computations
and other numerical computations.
We also compute the interaction of a vortex pair
with a circular cylinder to illustrate the simplicity of our method.
In chapter 9 we discuss the advantages of the redistribution method
compared to other particle methods.
Finally, in chapter 10 we give our conclusions.
