期刊
ACM TRANSACTIONS ON GRAPHICS
卷 41, 期 6, 页码 -出版社
ASSOC COMPUTING MACHINERY
DOI: 10.1145/3550454.3555459
关键词
curve dynamics; implicit representation; Clebsch variables; fluid dynamics; vortex filaments
资金
- European Research Council (ERC Consolidator Grant) [101045083]
- European Research Council (ERC) [101045083] Funding Source: European Research Council (ERC)
This paper presents a new method for representing curve dynamics, which uses an implicit description of curves to improve numerical stability and handle topological changes and re-connection events.
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.
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