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Efficient odd–even multigrid for pointwise incompressible fluid simulation on GPU

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Abstract

Fluid simulation is a well-established research field in computer graphics that aims to generate realistic and visually appealing simulations of fluids, including water, smoke, and fire. Divergence is identified as a crucial factor in achieving realistic fluid behavior. This article presents a GPU optimization of the pointwise incompressible fluid simulation technique, which uses pointwise incompressible velocity interpolation to ensure divergence at arbitrary points, rather than grid cells. Pointwise incompressible velocity interpolation at arbitrary points is the curl of velocity potential. The velocity potential can be obtained from the divergence-free velocities by solving a Poisson equation. To enhance the computational efficiency of the simulation, an odd–even geometric multigrid method is introduced to solve Poisson’s equation on non-power-of-2 resolution grids. Additionally, to recover the potential on grid cells, a warp-level method is proposed via divergence-free velocities on grid cells. The proposed warp-level potential recovery method offers GPU optimization and enhanced efficiency, in contrast to the sweeping method that only provides CPU optimization for potential recovery. Furthermore, a locally enhanced method is proposed to recover the detailed velocity potential within small domains through the use of the odd–even multigrid. The experiments show that the odd–even multigrid outperforms Weber’s multigrid by an average speedup factor of 4.32 across various grid sizes. On the other hand, the warp-level potential recovery method demonstrates notable speedups ranging from approximately 2–6 times for 2D grids and about 1.35–2.64 times for 3D grids when compared to the parallel sweeping method on GPU. The results of these contributions demonstrate remarkable improvements in the efficiency and performance of fluid simulations in computer graphics, harnessing the computational capabilities of modern GPUs to achieve visually appealing and realistic fluid behaviors.

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Acknowledgements

This work was funded in part by the Science and Technology Development Fund, Macau SAR (Grant no. 0075/2023/AMJ, 0003/2023/RIB1, 001/2024/SKL), in part by NSFC (62332015, 62072449), in part by the Guangdong Science and Technology Department (Grant no. 2020B1515130001), in part by the Zhuhai Science and Technology Innovation Bureau (Grant no. ZH2220004002524), in part by the International Science and Technology project of Guangzhou Development District (Grant no. 2022GH09), in part by Zhuhai UM Research Institute (Grant no. HF-011-2021), in part by the University of Macau (Grant No.: MYRG2022-00059-FST, MYRG-GRG2023-00237-FST-UMDF), and in part by the Fund of China University of Petroleum (Grant No. 21CX06042A).

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Authors and Affiliations

  1. State Key Laboratory of Internet of Things for Smart City & Centre for AI and Robotics, University of Macau, Macao, 999078, China

    Luan Lyu & Zhi-Xin Yang

  2. Faculty of Science and Technology, University of Macau, Macao, 999078, China

    Luan Lyu, Enhua Wu & Zhi-Xin Yang

  3. College of Computer Science and Technology, China University of Petroleum, Qingdao, 266580, China

    Wei Cao

  4. Multimedia Research Center, Tencent, Shenzhen, 518000, China

    Xiaohua Ren

  5. State Key Laboratory of Computer Science, Institute of Software, Chinese Academy of Sciences, Beijing, 100190, China

    Enhua Wu

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  1. Luan Lyu
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Correspondence to Enhua Wu or Zhi-Xin Yang.

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Lyu, L., Cao, W., Ren, X. et al. Efficient odd–even multigrid for pointwise incompressible fluid simulation on GPU. Vis Comput (2024). https://doi.org/10.1007/s00371-024-03264-y

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