Numerical Simulation of Hydrodynamics by the Method of Point Vortices

Abstract

The motion of a two-dimensional incompressible inviscid and homogeneous fluid can be thought of in terms of the gradual evolution of a continuous vorticity distribution, each scalar vortex element interacting with every other by an instantaneous action at a distance law. It is of particular interest that this model can be expressed in Hamiltonian form and that it shows many analogies with similar systems in plasma physics. In addition to the standard mesh techniques, a computational description can be obtained if the continuous vorticity distribution is replaced by a finite set of point vortices interacting through a stream function which satisfies Poisson's equation. The point vortices move in a velocity field given on a Cartesian mesh such that there is a close resemblance to particle models used in plasma simulations. The point vortex model is presented with a calculation on a test model and the sources of numerical errors are explained. Graphical results from several calculations are shown and it is concluded that the point vortex model is useful and versatile for a variety of problems in hydrodynamics as well as in plasma physics.