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DTSTART:18871231T000000
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DTSTAMP:20230103T035311Z
LOCATION:Room 325-AB\, Level 3\, West Wing
DTSTART;TZID=Asia/Seoul:20221208T153000
DTEND;TZID=Asia/Seoul:20221208T170000
UID:siggraphasia_SIGGRAPH Asia 2022_sess170_papers_252@linklings.com
SUMMARY:Hidden Degrees of Freedom in Implicit Vortex Filaments
DESCRIPTION:Technical Papers\n\nHidden Degrees of Freedom in Implicit Vort
ex Filaments\n\nIshida, Wojtan, Chern\n\nThis paper presents a new represe
ntation of curve dynamics, with applications to vortex filaments in fluid
dynamics. Instead of representing these filaments with explicit curve geom
etry and Lagrangian equations of motion, we represent curves implicitly wi
th a new co-dimensional 2 level set description. Our implicit representati
on admits several redundant mathematical degrees of freedom in both the co
nfiguration and the dynamics of the curves, which can be tailored specific
ally 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 perfect
ly map to a Clebsch representation in fluid dynamics. Motivated by these o
bservations, we introduce untwisted level set functions and non-swirling d
ynamics which successfully regularize sources of numerical instability, pa
rticularly 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 chan
ges and re-connection events.\n\nRegistration Category: FULL ACCESS, ON-DE
MAND ACCESS\n\nLanguage: ENGLISH\n\nFormat: IN-PERSON, ON-DEMAND
URL:https://sa2022.siggraph.org/en/full-program/?id=papers_252&sess=sess17
0
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