Andrew Cahaly , Fabien Evrard , Olivier Desjardins
{"title":"PLIC-Net:流体容积法中三维界面重建的机器学习方法","authors":"Andrew Cahaly , Fabien Evrard , Olivier Desjardins","doi":"10.1016/j.ijmultiphaseflow.2024.104888","DOIUrl":null,"url":null,"abstract":"<div><p>The accurate reconstruction of immiscible fluid–fluid interfaces from the volume fraction field is a critical component of geometric Volume of Fluid 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 <span><math><mrow><mn>3</mn><mo>×</mo><mn>3</mn><mo>×</mo><mn>3</mn></mrow></math></span> 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 <span><math><mrow><mi>O</mi><mrow><mo>(</mo><mn>1</mn><msup><mrow><mn>0</mn></mrow><mrow><mn>6</mn></mrow></msup><mo>)</mo></mrow></mrow></math></span> randomized paraboloid surfaces, which allows for the sampling a broad range of interface shapes. PLIC-Net is tested in multiphase flow simulations where it is compared to standard LVIRA and ELVIRA 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 LVIRA and ELVIRA. These results establish that machine learning is a viable approach to Volume of Fluid interface reconstruction and is superior to current reconstruction algorithms for some cases.</p></div>","PeriodicalId":339,"journal":{"name":"International Journal of Multiphase Flow","volume":null,"pages":null},"PeriodicalIF":3.6000,"publicationDate":"2024-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"PLIC-Net: A machine learning approach for 3D interface reconstruction in volume of fluid methods\",\"authors\":\"Andrew Cahaly , Fabien Evrard , Olivier Desjardins\",\"doi\":\"10.1016/j.ijmultiphaseflow.2024.104888\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>The accurate reconstruction of immiscible fluid–fluid interfaces from the volume fraction field is a critical component of geometric Volume of Fluid 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 <span><math><mrow><mn>3</mn><mo>×</mo><mn>3</mn><mo>×</mo><mn>3</mn></mrow></math></span> 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 <span><math><mrow><mi>O</mi><mrow><mo>(</mo><mn>1</mn><msup><mrow><mn>0</mn></mrow><mrow><mn>6</mn></mrow></msup><mo>)</mo></mrow></mrow></math></span> randomized paraboloid surfaces, which allows for the sampling a broad range of interface shapes. PLIC-Net is tested in multiphase flow simulations where it is compared to standard LVIRA and ELVIRA 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 LVIRA and ELVIRA. These results establish that machine learning is a viable approach to Volume of Fluid interface reconstruction and is superior to current reconstruction algorithms for some cases.</p></div>\",\"PeriodicalId\":339,\"journal\":{\"name\":\"International Journal of Multiphase Flow\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":3.6000,\"publicationDate\":\"2024-06-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Journal of Multiphase Flow\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0301932224001654\",\"RegionNum\":2,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MECHANICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Multiphase Flow","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0301932224001654","RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MECHANICS","Score":null,"Total":0}
PLIC-Net: A machine learning approach for 3D interface reconstruction in volume of fluid methods
The accurate reconstruction of immiscible fluid–fluid interfaces from the volume fraction field is a critical component of geometric Volume of Fluid 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 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 randomized paraboloid surfaces, which allows for the sampling a broad range of interface shapes. PLIC-Net is tested in multiphase flow simulations where it is compared to standard LVIRA and ELVIRA 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 LVIRA and ELVIRA. These results establish that machine learning is a viable approach to Volume of Fluid interface reconstruction and is superior to current reconstruction algorithms for some cases.
期刊介绍:
The International Journal of Multiphase Flow publishes analytical, numerical and experimental articles of lasting interest. The scope of the journal includes all aspects of mass, momentum and energy exchange phenomena among different phases such as occur in disperse flows, gas–liquid and liquid–liquid flows, flows in porous media, boiling, granular flows and others.
The journal publishes full papers, brief communications and conference announcements.