Visual
Computing
Computing
ACM Transactions on Graphics (Siggraph Asia 2022)
This paper presents a new representation of curve dynamics, with applications to vortex filaments in fluid dynamics. Instead of representing these filaments with explicit curve geometry and Lagrangian equations of motion, we represent curves implicitly with a new co-dimensional 2 level set description. Our implicit representation admits several redundant mathematical degrees of freedom in both the configuration and the dynamics of the curves, which can be tailored specifically to improve numerical robustness, in contrast to naive approaches for implicit curve dynamics that suffer from overwhelming numerical stability problems. Furthermore, we note how these hidden degrees of freedom perfectly map to a Clebsch representation in fluid dynamics. Motivated by these observations, we introduce untwisted level set functions and non-swirling dynamics which successfully regularize sources of numerical instability, particularly in the twisting modes around curve filaments. A consequence is a novel simulation method which produces stable dynamics for large numbers of interacting vortex filaments and effortlessly handles topological changes and re-connection events.
@article{
iwc2022implicit_filaments,
title = Hidden Degrees of Freedom in Implicit Vortex Filaments,
author = {Sadashige Ishida and Chris Wojtan and Albert Chern}
journal = {ACM Transactions on Graphics},
year = 2022,
volume = 41,
number = 6,
pages = {241:1--241:14},
articleno = 241,
url = {http://dx.doi.org/10.1145/3550454.3555459},
doi = {10.1145/3550454.3555459},
publisher = {ACM}
}
We thank the visual computing group at IST Austria for their valuable discussions and feedback. Houdini Education licenses were provided by SideFX software. This project was funded in part by the European Research Council (ERC Consolidator Grant 101045083 CoDiNA).
