A Practical Octree Liquid Simulator with Adaptive Surface Resolution

摘要

We propose a new adaptive liquid simulation framework that achieves highlydetailed behavior with reduced implementation complexity. Prior work hasshown that spatially adaptive grids are efficient for simulating large-scaleliquid scenarios, but in order to enable adaptivity along the liquid surfacethese methods require either expensive boundary-conforming (re-)meshingor elaborate treatments for second order accurate interface conditions. This complexity greatly increases the difficulty of implementation and maintainability,potentially making it infeasible for practitioners. We thereforepresent new algorithms for adaptive simulation that are comparatively easyto implement yet efficiently yield high quality results. First, we develop anovel staggered octree Poisson discretization for free surfaces that is secondorder in pressure and gives smooth surface motions even across octreeT-junctions, without a power/Voronoi diagram construction. We augmentthis discretization with an adaptivity-compatible surface tension force thatlikewise supports T-junctions. Second, we propose a moving least squaresstrategy for level set and velocity interpolation that requires minimal knowledgeof the local tree structure while blending near-seamlessly with standardtrilinear interpolation in uniform regions. Finally, to maximally exploit theflexibility of our new surface-adaptive solver, we propose several novelextensions to sizing function design that enhance its effectiveness and flexibility.We perform a range of rigorous numerical experiments to evaluatethe reliability and limitations of our method, as well as demonstrating it onseveral complex high-resolution liquid animation scenarios.