PLIC-Net: A Machine Learning Approach for 3D Interface Reconstruction in Volume of Fluid Methods
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arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866910552618434560 |
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| author | Cahaly, Andrew Evrard, Fabien Desjardins, Olivier |
| author_facet | Cahaly, Andrew Evrard, Fabien Desjardins, Olivier |
| contents | The accurate reconstruction of immiscible fluid-fluid interfaces from the volume fraction field is a critical component of geometric Volume of Fluid (VOF) methods. A common strategy is the Piecewise Linear Interface Calculation (PLIC), which fits a plane in each mixed-phase computational cell. However, recent work goes beyond PLIC by using two planes or even a paraboloid. To select such planes or paraboloids, complex optimization algorithms as well as carefully crafted heuristics are necessary. Yet, the potential exists for a well-trained machine learning model to efficiently provide broadly applicable solutions to the interface reconstruction problem at lower costs. In this work, the viability of a machine learning approach is demonstrated in the context of a single plane reconstruction. A feed-forward deep neural network is used to predict the normal vector of a PLIC plane given volume fraction and phasic barycenter data in a $3\times3\times3$ stencil. The PLIC plane is then translated in its cell to ensure exact volume conservation. Our proposed neural network PLIC reconstruction (PLIC-Net) is equivariant to reflections about the Cartesian planes. Training data is analytically generated with $\mathcal{O}(10^6)$ randomized paraboloid surfaces, which allows for sampling a wide range of interface shapes. PLIC-Net is tested in multiphase flow simulations where it is compared to standard (E)LVIRA reconstruction algorithms, and the impact of training data statistics on PLIC-Net's performance is also explored. It is found that PLIC-Net greatly limits the formation of spurious planes and generates cleaner numerical break-up of the interface. Additionally, the computational cost of PLIC-Net is lower than that of (E)LVIRA. These results establish that machine learning is a viable approach to VOF interface reconstruction and is superior to current reconstruction algorithms for some cases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_01383 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | PLIC-Net: A Machine Learning Approach for 3D Interface Reconstruction in Volume of Fluid Methods Cahaly, Andrew Evrard, Fabien Desjardins, Olivier Computational Physics Fluid Dynamics The accurate reconstruction of immiscible fluid-fluid interfaces from the volume fraction field is a critical component of geometric Volume of Fluid (VOF) methods. A common strategy is the Piecewise Linear Interface Calculation (PLIC), which fits a plane in each mixed-phase computational cell. However, recent work goes beyond PLIC by using two planes or even a paraboloid. To select such planes or paraboloids, complex optimization algorithms as well as carefully crafted heuristics are necessary. Yet, the potential exists for a well-trained machine learning model to efficiently provide broadly applicable solutions to the interface reconstruction problem at lower costs. In this work, the viability of a machine learning approach is demonstrated in the context of a single plane reconstruction. A feed-forward deep neural network is used to predict the normal vector of a PLIC plane given volume fraction and phasic barycenter data in a $3\times3\times3$ stencil. The PLIC plane is then translated in its cell to ensure exact volume conservation. Our proposed neural network PLIC reconstruction (PLIC-Net) is equivariant to reflections about the Cartesian planes. Training data is analytically generated with $\mathcal{O}(10^6)$ randomized paraboloid surfaces, which allows for sampling a wide range of interface shapes. PLIC-Net is tested in multiphase flow simulations where it is compared to standard (E)LVIRA reconstruction algorithms, and the impact of training data statistics on PLIC-Net's performance is also explored. It is found that PLIC-Net greatly limits the formation of spurious planes and generates cleaner numerical break-up of the interface. Additionally, the computational cost of PLIC-Net is lower than that of (E)LVIRA. These results establish that machine learning is a viable approach to VOF interface reconstruction and is superior to current reconstruction algorithms for some cases. |
| title | PLIC-Net: A Machine Learning Approach for 3D Interface Reconstruction in Volume of Fluid Methods |
| topic | Computational Physics Fluid Dynamics |
| url | https://arxiv.org/abs/2408.01383 |