Using statistical learning to close two-fluid multiphase flow equations for a simple bubbly system

Direct numerical simulations of bubbly multiphase flows are used to find closure terms for a simple model of the average flow, using Neural Networks (NNs). The flow considered consists of several nearly spherical bubbles rising in a periodic domain where the initial vertical velocity and the average bubble density are homogeneous in two directions but non-uniform in one of the horizontal directions. After an initial transient motion the average void fraction and vertical velocity become approximately uniform. The NN is trained on a dataset from one simulation and then used to simulate the evolution of other initial conditions. Overall, the resulting model predicts the evolution of the various initial conditions reasonably well.