Inferring incompressible two-phase flow fields from the interface motion using physics-informed neural networks
This work addresses the inverse modeling challenge for two-phase flows, which is important for fluid dynamics applications, but it is incremental as it applies existing PINN methods to this specific domain.
The authors tackled the problem of inferring velocity and pressure fields in incompressible two-phase flows from interface motion data using physics-informed neural networks, achieving successful results in both forward and inverse problems for classical test cases like drop in shear flow and rising bubble.
In this work, physics-informed neural networks are applied to incompressible two-phase flow problems. We investigate the forward problem, where the governing equations are solved from initial and boundary conditions, as well as the inverse problem, where continuous velocity and pressure fields are inferred from scattered-time data on the interface position. We employ a volume of fluid approach, i.e. the auxiliary variable here is the volume fraction of the fluids within each phase. For the forward problem, we solve the two-phase Couette and Poiseuille flow. For the inverse problem, three classical test cases for two-phase modeling are investigated: (i) drop in a shear flow, (ii) oscillating drop and (iii) rising bubble. Data of the interface position over time is generated by numerical simulation. An effective way to distribute spatial training points to fit the interface, i.e. the volume fraction field, and the residual points is proposed. Furthermore, we show that appropriate weighting of losses associated with the residual of the partial differential equations is crucial for successful training. The benefit of using adaptive activation functions is evaluated for both the forward and inverse problem.