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On the computation of vortex sheet evolutionPDE and Applied Math Seminar
|Speaker: ||Monika Nitsche, University of New Mexico|
|Location: ||1147 MSB|
|Start time: ||Thu, May 29 2008, 11:00AM|
A vortex sheet is a model for a shear flow which represents
a thin layer of vorticity by a surface of zero thickness in inviscid
flow. Under the governing Euler Equations the vortex sheets generically
develop singularities in finite time. With the goal of approximating
the shear flows past singularity formation the govering equations are
regularized. Various regularizations are possible.
In this talk I will discuss two issues that arise in vortex sheet
computations. The first regards the onset of irregular chaotic motion
in the regularized flow. I will present results using various regularizations and discuss open questions about the dependence of the behaviour on the regularization. The second issue regards large errors introduced in axisymmetric unregularized computations due to the singularity of the axisymmetric coordinate system on the axis. I will describe the errors and their origins, and present a method to resolve them.