Lagrangian Simulations of Fluids and Plasmas
(Robert Krasny, University of Michigan)

This talk describes recent Lagrangian simulations of incompressible fluids and
electrostatic collisionless plasmas. In both cases, the standard Eulerian
formulation is replaced by a Lagrangian formulation in terms of the flow map.
This leads naturally to a particle discretization. The particles carry
vorticity in the case of a fluid and electric charge in the case of a plasma.
The induced velocity and electric field are expressed as singular integrals.
The numerical method uses kernel smoothing for stability, adaptive particle
insertion for accuracy, and a multipole treecode for efficiency. Examples to
be presented include electron beams in 1D plasmas, and vortex sheets and
vortex rings in 2D and 3D fluids. The Lagrangian approach gives direct access
to dynamics, revealing the onset of chaos in these flows.