A Monte Carlo Method for Fluid Simulation

McGill University
University of Waterloo
Tümay Özdemir
University of Waterloo
Osaka University
University of Waterloo
McGill University
University of Waterloo

*Joint first authors

In ACM SIGGRAPH Asia, 2022

Abstract

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.

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Cite

@article{Rioux-Lavoie:2022:MCFluid,
    author = {Rioux-Lavoie, Damien and Sugimoto, Ryusuke and Özdemir, Tümay and Shimada, Naoharu H. and Batty, Christopher and Nowrouzezahrai, Derek and Hachisuka, Toshiya },
    title = {A Monte Carlo Method for Fluid Simulation},
    journal = {ACM Transactions on Graphics},
    volume = {41},
    number = {6},
    year = {2022},
    month = dec,
    doi = {10.1145/3550454.3555450},
}
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