Abstract
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.
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Acknowledgements
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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Takahiro Sato is an M.S. student at Computer Science Department, the University of Tokyo. His research interest is focused on physics simulation for applications in computer graphics.
Christopher Batty is an assistant professor of computer science at the University of Waterloo. His research is focused on the development of novel physical simulation techniques for applications in computer graphics and computational physics, with an emphasis on the diverse behaviors of fluids.
Takeo Igarashi is a professor at Computer Science Department, the University of Tokyo. He received his Ph.D. degree from Information Engineering Department, the University of Tokyo, in 2000. His research interest is in user interface in general and current focus is on interaction techniques for 3D graphics.
Ryoichi Ando is an assistant professor at National Institute of Informatics. His research interest is focused on physics simulation for computer graphics, with a strong emphasis on fluid animation.
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Sato, T., Batty, C., Igarashi, T. et al. Spatially adaptive long-term semi-Lagrangian method for accurate velocity advection. Comp. Visual Media 4, 223–230 (2018). https://doi.org/10.1007/s41095-018-0117-9
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DOI: https://doi.org/10.1007/s41095-018-0117-9