Multiphase flows of N immiscible incompressible fluids: An outflow/open boundary condition and algorithm

In this talk, we introduce a set of effective outflow/open boundary conditions, which is suitable for simulating multiphase flows of N (N≥2) immiscible incompressible fluids in domains involving outflows or open boundaries. These boundary conditions satisfy two properties: energy stability and reduction consistency. They are devised such that their contributions to the N-phase energy balance equation will not cause the total system energy to increase over time. Therefore, these outflow/open boundary conditions are very effective in overcoming the backflow instability. The reduction consistency ensures the inherent equivalence relations between N-phase system and the corresponding smaller system when some of the fluid components are absent from the N-phase system. We also present an efficient algorithm for numerically treating the proposed boundary conditions together with the N-phase governing equations. The proposed algorithm involves only solving a set of de-coupled individual Helmholtz equations in each time step with constant and time-independent coefficients. We present ample numerical examples to confirm that the proposed method produces physically accurate results.