Accurate Viscous Free Surfaces for Buckling,
Coiling, and Rotating Liquids

A stream of highly viscous liquid spontaneously coils and buckles due to the
application of correct traction free boundary conditions at the liquid-air interface.

Abstract: We present a fully implicit Eulerian technique for simulating free surface viscous liquids which eliminates artifacts in previous approaches, efficiently supports variable viscosity, and allows the simulation of more compelling viscous behaviour than previously achieved in graphics. Our method exploits a variational principle which automatically enforces the complex boundary condition on the shear stress at the free surface, while giving rise to a simple discretization with a symmetric positive definite linear system. We demonstrate examples of our technique capturing realistic buckling, folding and coiling behavior. In addition, we explain how to handle domains whose boundary comprises both ghost fluid Dirichlet and variational Neumann parts, allowing correct behaviour at free surfaces and solid walls for both our viscous solve and the variational pressure projection of [Batty et al. 2007].

Paper: PDF

Talk: Powerpoint

Video: Quicktime

Sample Code: Viscosity2D
A 2D implementation of our approach, built on top of a very simple free surface liquid simulator.

Christopher Batty - University of British Columbia
Robert Bridson - University of British Columbia

Citation: C. Batty and R. Bridson. Accurate Viscous Free Surfaces for Buckling, Coiling and Rotating Liquids. In Proceedings of ACM/Eurographics Symposium on Computer Animation, 2008.


 author = {Christopher Batty and Robert Bridson},
 title = {Accurate Viscous Free Surfaces for Buckling, Coiling, and Rotating Liquids},
 booktitle = {Proceedings of the 2008 ACM/Eurographics Symposium on Computer Animation},
 pages = {219--228},
 year = {2008},
 month = {July},

Natural Sciences and Engineering Research Council of Canada

Related Projects:
A Fast Variational Framework for Accurate Solid-Fluid Coupling
This paper introduces the idea of using a variational principle in combination with finite differences to easily capture a natural boundary condition using volume fractions. In this case, it is the solid boundary condition for pressure, whereas in the above paper the focus is on free surface boundary conditions for viscosity.

As of this writing (Dec 2010) this technique is used in two commercial software products, DPIT EFFEX and Exotic Matter's Naiad.