Quadtree Tall Cells for Eulerian Liquid Simulation

This paper introduces a novel grid structure that extends tall cell methods for efficient deep water simulation. Unlike previous tall cell methods, which are designed to capture all the fine details around liquid surfaces, our approach subdivides tall cells horizontally, allowing for more aggressive adaptivity and a significant reduction in the number of cells. The foundation of our method lies in a new variational formulation of Poisson’s equations for pressure solve tailored for tall-cell grids, which naturally handles the transition of variable-sized cells. This variational view not only permits the use of the efficacy-proven conjugate gradient method but also facilitates monolithic two-way coupled rigid bodies. The key distinction between our method and previous general adaptive approaches, such as tetrahedral or octree grids, is the simplification of adaptive grid construction. Our method performs grid subdivision in a quadtree fashion, rather than an octree. These 2D cells are then simply extended vertically to complete the tall cell population. We demonstrate that this novel form of adaptivity, which we refer to as quadtree tall cells, delivers superior performance compared to traditional uniform tall cells.