## Improved vortex methods for three-dimensional flows.(English)Zbl 0671.76025

Mathematical aspects of vortex dynamics, Proc. Workshop, Leesburg/VA 1988, 25-35 (1989).
Summary: [For the entire collection see Zbl 0668.00019.]
A major thrust of our research is to develop robust numerical methods for three-dimensional, incompressible vortical flows that use Lagrangian vortex elements. A successful scheme, for example, must be able to handle regions of intense vortex stretching and vortex reconnection with reasonable accuracy (certainly without diverging!) Here, we consider vortex particles, also commonly called vortons or vortex sticks. These are vector elements and to each element we associate a position vector and a strength vector (vorticity vector times volume). The element is convected with the local velocity and the strength vector is subjected to three dimensional vortex stretching according to the Helmholtz equation.
The following issues will be discussed: use of $$\delta$$-function elements and weak solutions of the vorticity equation, use of smoothed elements and the choice of the smoothing function, representation of viscous effects and the redistribution of element strengths and conservation laws - are they satisfied? The various proposed schemes have been tested on flows involving a strong interaction between two vortex rings.

### MSC:

 76B47 Vortex flows for incompressible inviscid fluids 76M99 Basic methods in fluid mechanics

Zbl 0668.00019