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Abstract:
A new version of the Barnes-Hut treecode algorithm will be described for
particle simulations of vortex sheet roll-up in 3D fluid flow. The vortex sheet
problem requires using a regularized Biot-Savart kernel in order to control the
shortwave Kelvin-Helmholtz instability. The treecode algorithm uses Taylor
expansions in Cartesian coordinates to approximate the particle-cluster
interactions. The necessary Taylor coefficients are computed using a recurrence
relation. Adaptive techniques are employed to gain efficiency, including
adaptive clusters and variable order expansions. Results will be presented
showing the azimuthal instability of a vortex ring. The algorithm is also being
applied to electrostatic force evaluation in molecular dynamics and plasma
dynamics, and these applications will be briefly described.
[LECTURE SLIDES]
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