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Velocity-Based Monte Carlo Fluids

Published: 13 July 2024 Publication History

Abstract

We present a velocity-based Monte Carlo fluid solver that overcomes the limitations of its existing vorticity-based counterpart. Because the velocity-based formulation is more commonly used in graphics, our Monte Carlo solver can be readily extended with various techniques from the fluid simulation literature. We derive our method by solving the Navier-Stokes equations via operator splitting and designing a pointwise Monte Carlo estimator for each substep. We reformulate the projection and diffusion steps as integration problems based on the recently introduced walk-on-boundary technique [Sugimoto et al. 2023]. We transform the volume integral arising from the source term of the pressure Poisson equation into a form more amenable to practical numerical evaluation. Our resulting velocity-based formulation allows for the proper simulation of scenes that the prior vorticity-based Monte Carlo method [Rioux-Lavoie et al. 2022] either simulates incorrectly or cannot support. We demonstrate that our method can easily incorporate advancements drawn from conventional non-Monte Carlo methods by showing how one can straightforwardly add buoyancy effects, divergence control capabilities, and numerical dissipation reduction methods, such as advection-reflection and PIC/FLIP methods.

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Cited By

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  • (2024)Projected Walk on Spheres: A Monte Carlo Closest Point Method for Surface PDEsSIGGRAPH Asia 2024 Conference Papers10.1145/3680528.3687599(1-10)Online publication date: 3-Dec-2024

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cover image ACM Conferences
SIGGRAPH '24: ACM SIGGRAPH 2024 Conference Papers
July 2024
1106 pages
ISBN:9798400705250
DOI:10.1145/3641519
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Published: 13 July 2024

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Author Tags

  1. Monte Carlo methods
  2. fluid simulation
  3. walk-on-boundary

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  • (2024)Projected Walk on Spheres: A Monte Carlo Closest Point Method for Surface PDEsSIGGRAPH Asia 2024 Conference Papers10.1145/3680528.3687599(1-10)Online publication date: 3-Dec-2024

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