A multi-layer grid approach for fluid animation

Real fluid phenomena often present multi-scale behavior, such as tiny splashes and foams in the ocean and small vortexes near the bank of a wide river, which requires sufficiently fine grids and long computational time in the simulation to get adequately resolved solution. We present a new method to address this issue by solving Navier-Stokes equation on multiple layers of grids with different resolutions or categories. The governing equations are solved on different layers in successive passes. And the velocity and pressure fields are synchronized between adjacent layers through the processes of prolongation and restriction. The multi-layer approach enables combining the respective advantages of various grid types, catching the multi-scale behavior of fluids and optimizing the computational resources. Two simple examples, the regular-tetrahedral and the coarse-fine bi-layer grids, are given to illustrate the powerfulness of the multi-layer framework.