Efficient and accurate machine learning models for volume of fluid (VOF) simulation on uniform Cartesian mesh

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In this paper, we describe a machine learning (ML) approach for estimating interface orientation in multiphase flow using the volume of fluid (VOF) method on a uniform Cartesian mesh. By using complex shapes generated with the parametric radial star formula during training, we significantly improve prediction accuracy without increasing the network's structural complexity or processing cost. Our key contribution is the development of a robust ML model capable of reliably predicting interface orientation angles on uniform Cartesian grids. To enhance performance and robustness, we conducted a parametric study of the ML models' hyperparameters. The proposed method produced two models: a full augmented (9-cell) stencil and a compact (5-cell) stencil. Both were compared against popular finite difference/volume methods commonly used in VOF schemes. The results show that our approach is more accurate while remaining computationally efficient, particularly when employing a small stencil. Numerical studies, including challenging flow scenarios, demonstrate that the technique can predict interface orientation with an absolute mean error of less than 1 degree. Implemented in the OpenFOAM isoAdvector, our technique reliably produces accurate interface tracking with minimal deviation from the exact solution. These findings highlight the potential for incorporating machine learning approaches into classical numerical methods to improve the accuracy and reliability of the VOF method in a variety of challenging applications using uniform Cartesian meshes.