A new doubly discrete analogue of smoke ring flow

doi:10.1088/1751-8113/40/42/S04

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

Ulrich Pinkall et al 2007 J. Phys. A: Math. Theor. 40 12563-12576 doi: 10.1088/1751-8113/40/42/S04

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Ulrich Pinkall, Boris Springborn and Steffen Weißmann
Institut für Mathematik, Technische Universität Berlin, Straße des 17. Juni 136, 10623 Berlin, Germany
E-mail: pinkall@math.tu-berlin.de, springb@math.tu-berlin.de and weissman@math.tu-berlin.de

Abstract. 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 discretization of the localized induction approximation of filament motion. This discretization 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.

PACS numbers: 02.30.Ik, 47.10.+g, 45.20.Jj

Mathematics Subject Classification: 76B47, 70H06

Print publication: Issue 42 (19 October 2007)
Received 15 January 2007, in final form 26 July 2007
Published 2 October 2007

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

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