Rioux-Lavoie, DamienSugimoto, RyusukeOzdemir, TumayShimada, Naoharu H.Batty, ChristopherNowrouzezahrai, DerekHachisuka, Toshiya2024-04-222024-04-222022-12https://doi.org/10.1145/3550454.3555450http://hdl.handle.net/10012/20464© 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.We 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.enmathematics of computingprobabilistic algorithmspartial differential equationscomputing methodologiesmodeling and simulationcomputational fluid dynamicsMonte Carlo integrationstochastic processeswalk-on-spheres algorithmArticle