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Research Article | Open Access

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

The University of Tokyo, Tokyo, Japan.
University of Waterloo, Waterloo, Canada.
National Institute of Informatics, Japan.
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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.

Keywords

fluid simulationadvectionmethod ofcharacteristicsspatially adaptive inte-grationinterpolation error correction

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41095_2018_117_MOESM1_ESM.mp4

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Computational Visual Media
Volume 4 Issue 3,
September 2018
Pages 223-230
DOI: 10.1007/s41095-018-0117-9

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Cite this article:
Sato T, Batty C, Igarashi T, et al. Spatially adaptive long-term semi-Lagrangian method for accurate velocity advection. Computational Visual Media, 2018, 4(3): 223-230. https://doi.org/10.1007/s41095-018-0117-9

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Revised: 31 January 2018
Accepted: 07 April 2018
Published: 06 August 2018
© The Author(s) 2018

This article is published with open access at Springerlink.com

The articles published in this journal are distributed under the terms of the Creative Commons Attribution 4.0 International License (http:// creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Other papers from this open access journal are available free of charge from http://www.springer.com/journal/41095. To submit a manuscript, please go to https://www. editorialmanager.com/cvmj.