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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/139598Modelling 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.15 pages, 3 figuresExactly Solvable and Integrable SystemsDynamical SystemsFluid DynamicsA new doubly discrete analogue of smoke ring flow and the real time simulation of fluid flowtext