{"scopus_import":"1","publisher":"Association for Computing Machinery","date_created":"2023-01-29T23:00:59Z","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","oa":1,"oa_version":"Published Version","status":"public","title":"Hidden degrees of freedom in implicit vortex filaments","quality_controlled":"1","tmp":{"image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"date_updated":"2023-08-04T09:37:23Z","article_processing_charge":"No","month":"12","day":"01","file":[{"date_updated":"2023-01-30T07:15:48Z","file_id":"12433","success":1,"date_created":"2023-01-30T07:15:48Z","file_size":15551202,"relation":"main_file","checksum":"a2fba257fdefe0e747182be6c0f7c70c","content_type":"application/pdf","file_name":"2022_ACM_Ishida.pdf","access_level":"open_access","creator":"dernst"}],"type":"journal_article","abstract":[{"text":"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.","lang":"eng"}],"department":[{"_id":"ChWo"}],"issue":"6","publication_status":"published","date_published":"2022-12-01T00:00:00Z","year":"2022","volume":41,"intvolume":"        41","ddc":["000"],"project":[{"_id":"34bc2376-11ca-11ed-8bc3-9a3b3961a088","name":"Computational Discovery of Numerical Algorithms for Animation and Simulation of Natural Phenomena","grant_number":"101045083"}],"isi":1,"file_date_updated":"2023-01-30T07:15:48Z","acknowledgement":"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).","publication_identifier":{"eissn":["1557-7368"],"issn":["0730-0301"]},"external_id":{"isi":["000891651900061"]},"doi":"10.1145/3550454.3555459","author":[{"id":"6F7C4B96-A8E9-11E9-A7CA-09ECE5697425","full_name":"Ishida, Sadashige","last_name":"Ishida","first_name":"Sadashige"},{"orcid":"0000-0001-6646-5546","first_name":"Christopher J","last_name":"Wojtan","full_name":"Wojtan, Christopher J","id":"3C61F1D2-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Albert","last_name":"Chern","full_name":"Chern, Albert"}],"publication":"ACM Transactions on Graphics","has_accepted_license":"1","language":[{"iso":"eng"}],"_id":"12431","article_number":"241","article_type":"original","citation":{"mla":"Ishida, Sadashige, et al. “Hidden Degrees of Freedom in Implicit Vortex Filaments.” <i>ACM Transactions on Graphics</i>, vol. 41, no. 6, 241, Association for Computing Machinery, 2022, doi:<a href=\"https://doi.org/10.1145/3550454.3555459\">10.1145/3550454.3555459</a>.","ieee":"S. Ishida, C. Wojtan, and A. Chern, “Hidden degrees of freedom in implicit vortex filaments,” <i>ACM Transactions on Graphics</i>, vol. 41, no. 6. Association for Computing Machinery, 2022.","chicago":"Ishida, Sadashige, Chris Wojtan, and Albert Chern. “Hidden Degrees of Freedom in Implicit Vortex Filaments.” <i>ACM Transactions on Graphics</i>. Association for Computing Machinery, 2022. <a href=\"https://doi.org/10.1145/3550454.3555459\">https://doi.org/10.1145/3550454.3555459</a>.","ista":"Ishida S, Wojtan C, Chern A. 2022. Hidden degrees of freedom in implicit vortex filaments. ACM Transactions on Graphics. 41(6), 241.","apa":"Ishida, S., Wojtan, C., &#38; Chern, A. (2022). Hidden degrees of freedom in implicit vortex filaments. <i>ACM Transactions on Graphics</i>. Association for Computing Machinery. <a href=\"https://doi.org/10.1145/3550454.3555459\">https://doi.org/10.1145/3550454.3555459</a>","ama":"Ishida S, Wojtan C, Chern A. Hidden degrees of freedom in implicit vortex filaments. <i>ACM Transactions on Graphics</i>. 2022;41(6). doi:<a href=\"https://doi.org/10.1145/3550454.3555459\">10.1145/3550454.3555459</a>","short":"S. Ishida, C. Wojtan, A. Chern, ACM Transactions on Graphics 41 (2022)."}}