Computing interface curvature from volume fractions: a machine learning approach

The volume of fluid (VOF) method is widely used to simulate the flow of immiscible fluids. It uses a discrete and sharp volume fractions field to represent the fluid-fluid interface on a Eulerian grid. The most challenging part of the VOF method is the accurate computation of the local interface curvature which is essential for evaluation of the surface tension force at the interface. In this paper, a machine learning approach is used to develop a model which predicts the local interface curvature from neighbouring volume fractions. A novel data generation methodology is devised which generates well-balanced randomized data sets comprising of spherical interface patches of different configurations/orientations. A two-layer feed-forward neural network with different network parameters is trained on these data sets and the developed models are tested for different shapes i.e. ellipsoid, 3D wave and Gaussian. The best model is selected on the basis of specific criteria and subsequently compared with conventional curvature computation methods (convolution and height function) to check the nature and grid convergence of the model. The model is also coupled with a multiphase flow solver to evaluate its performance using standard test cases: i) stationary bubble, ii) oscillating bubble and iii) rising bubble under gravity. Our results demonstrate that machine learning is a feasible approach for fairly accurate curvature computation. It easily outperforms the convolution method and even matches the accuracy of the height function method for some test cases