A Monte Carlo Method for Fluid Simulation
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Date
2022-12
Authors
Rioux-Lavoie, Damien
Sugimoto, Ryusuke
Ozdemir, Tumay
Shimada, Naoharu H.
Batty, Christopher
Nowrouzezahrai, Derek
Hachisuka, Toshiya
Journal Title
Journal ISSN
Volume Title
Publisher
Association for Computing Machinery
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.
Description
© Damien Rioux-Lavioe, Ryusuke Sugimoto, Tumay Ozdemir, Naoharu H. Shimada, Christopher Batty, Derek Nowrouzezahrai & Toshiya Hachisuka | 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, http://dx.doi.org/10.1145/3550454.3555450.
Keywords
mathematics of computing, probabilistic algorithms, partial differential equations, computing methodologies, modeling and simulation, computational fluid dynamics, Monte Carlo integration, stochastic processes, walk-on-spheres algorithm