PCNN: A physics-constrained neural network for multiphase flows

The present study develops a physics-constrained neural network (PCNN) to predict sequential patterns and motions of multiphase flows (MPFs), which includes strong interactions among various fluid phases. To predict the order parameters, which locate individual phases, in the future time, the conditional neural processes and long short-term memory (CNP-LSTM) are applied to quickly infer the dynamics of the phases after encoding only a few observations. After that, the multiphase consistent and conservative boundedness mapping algorithm (MCBOM) is implemented to correct the order parameters predicted from CNP-LSTM in order to strictly satisfy the mass conservation, the summation of the volume fractions of the phases to be unity, the consistency of reduction, and the boundedness of the order parameters. Then, the density of the fluid mixture is updated from the corrected order parameters. Finally, the velocity in the future time is predicted by a physics-informed CNP-LSTM (PICNP-LSTM) where conservation of momentum is included in the loss function with the observed density and velocity as the inputs. The proposed PCNN for MPFs sequentially performs (CNP-LSTM)-(MCBOM)-(PICNP-LSTM), which avoids unphysical behaviors of the order parameters, accelerates the convergence, and requires fewer data to make predictions. Numerical experiments demonstrate that the proposed PCNN is capable of predicting MPFs effectively.