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DTSTAMP:20230103T035307Z
LOCATION:Auditorium\, Level 5\, West Wing
DTSTART;TZID=Asia/Seoul:20221206T100000
DTEND;TZID=Asia/Seoul:20221206T120000
UID:siggraphasia_SIGGRAPH Asia 2022_sess153_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, EXPER
 IENCE PLUS ACCESS, EXPERIENCE ACCESS, TRADE EXHIBITOR\n\nLanguage: ENGLISH
 \n\nFormat: IN-PERSON
URL:https://sa2022.siggraph.org/en/full-program/?id=papers_252&sess=sess15
 3
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