Liquid Simulation on Lattice-based Tetrahedral Meshes (LSL)
Nuttapong Chentanez, Bryan Eric Feldman, Francois Labelle, James O'Brien and Jonathan Shewchuk
MICRO 03-067 and 04-066, National Science Foundation CCF-0430065 and CCF-0635381, Apple -, Pixar -, Intel -, Sony -, Hellman - and Alfred P. Sloan Fellowships -
This project explores a simulation method for animating the behavior of incompressible liquids with complex free surfaces. The region occupied by the liquid is discretized with a boundary-conforming tetrahedral mesh that grades from fine resolution near the surface to coarser resolution on the interior. At each time-step, semi-Lagrangian techniques are used to advect the fluid and its boundary forward, and a new conforming mesh is then constructed over the fluid-occupied region. The tetrahedral meshes are built using a variation of the body-centered cubic lattice structure that allows octree grading and deviation from the lattice-structure at boundaries. The semi-regular mesh structure can be generated rapidly and allows efficient computation and storage while still conforming well to boundaries and providing a mesh-quality guarantee. Pressure projection is performed using an algebraic multigrid method, and a thickening scheme is used to reduce volume loss when fluid features shrink below mesh resolution. Examples are provided to demonstrate that the resulting method can capture complex liquid motions that include fine detail on the free surfaces without suffering from excessive amounts of volume loss or artificial damping.
Figure 1: The upper-left image shows a wave of liquid flowing over a hemispherical obstacle. The upper-right image shows a cutaway view of the underlying tetrahedral simulation mesh which corresponds to the area outlined in green in the upper-left image. The two lower images correspond the small area outlined in yellow. The lower-left shows the surface triangulation used by the surface tracker and the lower-right shows the surface of the simulation mesh.
Figure 2: These images show two views of a liquid pouring down a pair of chutes and into a transparent container. The lower four images are a sequence from the animation which are evenly spaced in time.
- N. Chentanez, B. E. Feldman, F. Labelle, J. F. O'Brien, and J. R. Shewchuk, "Liquid Simulation on Lattice-Based Tetrahedral Meshes," Appeared in Proceedings of ACM SIGGRAPH/Eurographics Symposium on Computer Animation, San Diego, CA, August 2007.