Spatially adaptive long-term semi-Lagrangian method for accurate velocity advection
We introduce a new advection scheme for fluid animation. Our main contribution is the use of long-term temporal changes in pressure to extend the commonly used semi-Lagrangian scheme further back along the time axis. Our algorithm starts by tracing sample points along a trajectory following the velocity field backwards in time for many steps. During this backtracing process, the pressure gradient along the path is integrated to correct the velocity of the current time step. We show that our method effectively suppresses numerical diffusion, retains small-scale vorticity, and provides better long-term kinetic energy preservation.
Keywordsfluid simulation advection method of characteristics spatially adaptive integration interpolation error correction
This work was supported by NSERC (Grant RGPIN-04360-2014) and JSPS KAKENHI (Grant 17H00752). The authors thank Toshiya Hachisuka for insightful discussions.
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