Local interface remapping based curvature computation on unstructured grids in volume of fluid methods using machine learning

Abstract

The volume of fluid method is widely used for interface capturing in two-phase flows including surface tension. Calculation of surface forces requires accurate local interfacial curvature, which, despite receiving considerable attention, remains a challenge due to the abrupt variation of volume fraction near the interface. Based on recent studies showing the potential of data-driven techniques, a machine learning (ML) model using a multi-layered artificial neural network is initially developed to predict curvature on structured grids. Known shapes in the form of circular interface segments are used to generate a synthetic training dataset consisting of interfacial curvature and volume fractions. An optimum model configuration is carefully obtained, with a larger 5 × 5 input stencil showing increased accuracy for test data along with analytical test cases. However, an extension of the model to unstructured grids, required in simulations involving complex geometries, is non-trivial. To overcome the limitations, a local interface remapping algorithm is proposed where the stencil around a target cell is transformed into a structured stencil for the generation of the input dataset. The algorithm enables using the same ML model developed for structured grids to predict curvature on unstructured grids, thereby maintaining the simplicity of the ML strategy. The algorithm accurately predicts curvature for some analytically known shapes on quadrangular and triangular grids. Eventually, the ML model with the remapping algorithm is integrated into a two-phase flow solver to assess the performance in dynamic simulation environments, where satisfactory results are obtained for a benchmark rising bubble problem on both structured and unstructured grids.