This paper describes 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 volume loss or artificial damping.

Chentanez, N., Feldman, B.E., Labelle, F., O'Brien, J.F., Shewchuk, J. "Liquid Simulation on Lattice-Based Tetrahedral Meshes." In Proceedings of ACM SIGGRAPH/Eurographics Symposium on Computer Animation, pages 219-228, San Diego, August 3-4, 2007

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