Energy-Preserving Integrators for Fluid Animation
To appear in SIGGRAPH 2009
Abstract: Numerical viscosity has long been a problem in fluid animation. Existing methods suffer from intrinsic artificial dissipation and often apply complicated computational mechanisms to combat such effects. Consequently, dissipative behavior cannot be controlled or modeled explicitly in a manner independent of time step size, complicating the use of coarse previews and adaptive time-stepping methods. This paper proposes simple, unconditionally stable, fully Eulerian integration schemes with no numerical viscosity that are capable of maintaining the liveliness of fluid motion without recourse to corrective devices. Pressure and fluxes are solved efficiently and simultaneously in a time-reversible manner on simplicial grids, and the energy is preserved exactly over long time scales in the case of inviscid fluids. These integrators can be viewed as an extension of the classical energy-preserving Harlow-Welch / Crank- Nicolson scheme to simplicial grids.
The authors wish to thank our collaborators Eva Kanso and Jerrold E. Marsden, as well as Kevin Beason for his renderer Pane. This research was partially funded by the NSF (CCF-0811373/0811313, DMS-0453145, and CMMI-0757106/0757123), the DOE (DE-FG02-04ER25657), and Pixar.
Single frames rendered at higher quality:
Stills from the supplemental video: