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A Monte Carlo Method for Fluid Simulation

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dc.contributor.authorRioux-Lavoie, Damien
dc.contributor.authorSugimoto, Ryusuke
dc.contributor.authorOzdemir, Tumay
dc.contributor.authorShimada, Naoharu H.
dc.contributor.authorBatty, Christopher
dc.contributor.authorNowrouzezahrai, Derek
dc.contributor.authorHachisuka, Toshiya
dc.date.accessioned2024-04-22T14:44:32Z
dc.date.available2024-04-22T14:44:32Z
dc.date.issued2022-12
dc.description© ACM, 2022. This is the author's version of the work. It is posted here for your personal use. Not for redistribution. The definitive Version of Record was published in ACM Transactions on Graphics, https://doi.org/10.1145/3550454.3555450.en
dc.description.abstractWe present a novel Monte Carlo-based fluid simulation approach capable of pointwise and stochastic estimation of fluid motion. Drawing on the Feynman-Kac representation of the vorticity transport equation, we propose a recursive Monte Carlo estimator of the Biot-Savart law and extend it with a stream function formulation that allows us to treat free-slip boundary conditions using a Walk-on-Spheres algorithm. Inspired by the Monte Carlo literature in rendering, we design and compare variance reduction schemes suited to a fluid simulation context for the first time, show its applicability to complex boundary settings, and detail a simple and practical implementation with temporal grid caching. We validate the correctness of our approach via quantitative and qualitative evaluations - across a range of settings and domain geometries - and thoroughly explore its parameters' design space. Finally, we provide an in-depth discussion of several axes of future work building on this new numerical simulation modality.en
dc.description.sponsorshipNatural Sciences and Engineering Research Council of Canada.en
dc.identifier.urihttps://doi.org/10.1145/3550454.3555450
dc.identifier.urihttp://hdl.handle.net/10012/20464
dc.language.isoenen
dc.publisherAssociation for Computing Machineryen
dc.relation.ispartofseriesACM Transactions on Graphics;41(6)
dc.subjectmathematics of computingen
dc.subjectprobabilistic algorithmsen
dc.subjectpartial differential equationsen
dc.subjectcomputing methodologiesen
dc.subjectmodeling and simulationen
dc.subjectcomputational fluid dynamicsen
dc.subjectMonte Carlo integrationen
dc.subjectstochastic processesen
dc.subjectwalk-on-spheres algorithmen
dc.titleA Monte Carlo Method for Fluid Simulationen
dc.typeArticleen
dcterms.bibliographicCitationRioux-Lavoie, D., Sugimoto, R., Özdemir, T., Shimada, N. H., Batty, C., Nowrouzezahrai, D., & Hachisuka, T. (2022). A Monte Carlo method for fluid simulation. ACM Transactions on Graphics, 41(6), 1–16. https://doi.org/10.1145/3550454.3555450en
uws.contributor.affiliation1Faculty of Mathematicsen
uws.contributor.affiliation2David R. Cheriton School of Computer Scienceen
uws.peerReviewStatusRevieweden
uws.scholarLevelFacultyen
uws.typeOfResourceTexten

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