Spatially adaptive long-term semi-Lagrangian method for accurate velocity advection

Takahiro Sato

The University of Tokyo

Christopher Batty

University of Waterloo

Takeo Igarashi

The University of Tokyo

Ryoichi Ando

National Institute of Informatics

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.
Takahiro Sato, Christopher Batty, Takeo Igarashi and Ryoichi Ando. Computational Visual Media 2018.