Energy-Preserving Integrators for Fluid Animation

Energy-Preserving Integrators for Fluid Animation
Patrick Mullen, Keenan Crane, Dmitry Pavlov, Yiying Tong, Mathieu Desbrun
http://users.cms.caltech.edu/~keenan/project_epifa.html

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. Our method is simple, unconditionally stable, and fully Eulerian. It exhibits no numerical viscosity and is 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.

This video illustrates the conservation properties and time symmetry of our integrator, provides comparisons to other fluid simulation methods, and demonstrates applications to computer graphics.

Category:

Science & Technology

Tags:

• fluid simulation
• computer animation
• numerical simulation
• computer graphics
• fluid solver
• integrator
• variational integrator
• 3d graphics
• smoke
• stanford bunny
• Taylor vortices
• incompressible fluid
• Euler equations
• Navier-Stokes

[TheFerruccio]

Was exterior calculus employed with this, turning the continuous quantities that have to be integrated into discrete quantities along the boundaries of domains? Excuse my ignorance on this. This is very fascinating how these calculations are done. How long do you suspect it will take before this can be done in real time, 3 dimensions, with volume domains (like tets)?

[niiidar]

Interesting.

Fluid dynamics has to be the most advanced dynamics, ever.