Curvature Estimation Modeling Using Machine Learning for CLSVOF Method: Comparison With Conventional Methods

Despite extensive progress in recent decades, curvature estimation in two-phase models remains a challenge. Well-established curvature computing techniques such as distance function, smoothed volume fraction and height-function directly estimate the interface curvature from the implicit representation of the interface. Most recently, machine learning approach has been incorporated in computational physics simulation. Machine learning is a set of algorithms that can be utilized for training a system which allows predicting the output in the future. In this work, we train a curvature estimation model using machine learning approach for Coupled Level Set Volume of Fluid (CLSVOF) method in which both distance function and volume fraction implicitly represent the interface. Three datasets for the curvature are generated: a) curvature as a function of volume fraction (nine inputs), b) curvature as a function of distance function (nine inputs), and c) curvature as a function of both volume fraction and distance function (eighteen inputs). For each interfacial cell, curvature and input parameters (nine volume fraction and nine distance function values) at nine grid points across the interface are stored. Datasets are utilized to train different curvature computing models using neural network (NN) learning algorithm. Comparison of different datasets reveals that the distance function dataset is the best input for curvature function training. Different available learning algorithms on built-in NN toolbox in Matlab are examined. The curvature estimation function is examined for a dimensional 2D well-defined droplet on different grid resolution. In addition, the curvature estimation model by machine learning approach is compared with conventional methods such as the level set method and height function method for couple of cases. First, the case of elliptical droplet is used to evaluate curvature estimation of different methods in comparison with the analytical solution. Then, the standard case of equilibrium droplet is simulated by CLSVOF solver using different curvature estimation methods to evaluate parasitic currents generation and droplet pressure prediction. The results show that the machine learning curvature function outperforms conventional methods even on coarse grids. Finally, the curvature estimation methods are is utilized to solve a practical case of rising bubble. We observed that the terminal velocity of capped bubble reported by curvature function simulation has the lowest error.