A new doubly discrete analogue of smoke ring flow and the real time simulation of fluid flow

Details A new doubly discrete analogue of smoke ring flow and the real time simulation of fluid flow A new doubly discrete analogue of smoke ring flow and the real time simulation of fluid flow

2007-08-07

arxiv.org/abs/0708.0979v1

J. Phys. A: Math. Theor. 40 (2007) 12563-12576

Nonlinear Sciences

Exactly Solvable and Integrable Systems

15 pages, 3 figures

Scientific paper

10.1088/1751-8113/40/42/S04

Modelling incompressible ideal fluids as a finite collection of vortex filaments is important in physics (super-fluidity, models for the onset of turbulence) as well as for numerical algorithms used in computer graphics for the real time simulation of smoke. Here we introduce a time-discrete evolution equation for arbitrary closed polygons in 3-space that is a discretisation of the localised induction approximation of filament motion. This discretisation shares with its continuum limit the property that it is a completely integrable system. We apply this polygon evolution to a significant improvement of the numerical algorithms used in Computer Graphics.

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