Abstract: The first part of the talk presents simulations of elliptical fluid vortices described by the 2D incompressible Euler equations where an open question is whether such vortices evolve into an axisymmetric state. The second part of the talk presents simulations of collisionless electrostatic plasmas governed by the 1D1V Vlasov-Poisson equations applied to Landau damping and halo formation in an ion beam. The fluid calculations use a recently developed version of Chorin's vortex method and those techniques were adapted to do the plasma simulations. The techniques include (1) a particle/panel representation of the fluid vorticity in physical space and the plasma particle distribution function in phase space, (2) semi-Lagrangian time-stepping with tree-based adaptive mesh refinement, (3) regularized integral-based calculation of the velocity field and electric field, (4) GPU-accelerated barycentric Lagrange treecode.

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