Batty, ChristopherBridson, Robert2021-02-032021-02-032008-07https://dl.acm.org/doi/10.5555/1632592.1632624?cid=81320487818http://hdl.handle.net/10012/16791© Christopher Batty & Robert Bridson | ACM 2008. This is the author's version of the work. It is posted here for your personal use. Not for redistribution. The definitive Version of Record was published in SCA '08: Proceedings of the 2008 ACM SIGGRAPH/Eurographics Symposium on Computer Animation, https://dl.acm.org/doi/10.5555/1632592.1632624?cid=81320487818.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. [BBB07].enArticle