CDS/CIMMS Lunchtime Seminar: Integrable systems for real time simulation of fluid flow

Dr. Ulrich Pinkall
Arbeitsgruppe Geometrie
Institut für Mathematik
Technische Universität Berlin

Around 1910 Levi Civita and his student da Rios derived an evolution equation for closed space curves (nowadays called the smoke ring flow) that models the movement of an infinitely thin vortex filament in an ideal fluid. It has turned out that this smoke ring flow has lots of conserved quantities (among them the length and the total squared curvature) and is in fact a completely integrable Hamiltonian system.
                                                                                
Here we present a discretization of the smoke ring flow (an integrable system on its own) and show how it can be applied to develop fast algorithms useful in Computer Graphics to model physically correct fluid motion (like smoke) in real time.