Machine-learning-based surface tension model for multiphase flow simulation using particle method

Particle methods have shown their potential for simulating multiphase flows due to the convenience in capturing interfaces. However, when it comes to estimate the surface tension, calculation of the curvature of the interface remains challenging. Traditional methods are based on derivative models to estimate the curvature analytically from the particle number density or color function that marks different phases. It is difficult to estimate the curvature accurately in traditional derivative models. In this study, background cells are built up and are used to predict the curvature through machine learning. By training on a data set generated using circles of varying sizes, a relation function is found to predict the curvature from the particle distribution near the interface. Together with the enhanced schemes developed in our previous study, multiphase flows with surface tension are studied within the framework of the moving particle semi-implicit method.