An ALE–PFEM method for the numerical simulation of two-phase mixture flow

A new finite element method is proposed to simulate two-phase mixture problems with free surfaces and/or large moving boundaries. The two phases are treated as interpenetrating continua within a two-fluid model. In contrast to the conventional two-fluid model formulations, in which the governing equations are written in the Eulerian–Eulerian description, the modified two-fluid model has the governing equations of one fluid phase written in the Lagrangian description while the respective equations of the other phase is formulated in the Arbitrary Lagrangian–Eulerian (ALE) description with relative velocities defined with respect to the moving mesh associated with the first fluid phase. The Finite Element Method (FEM) together with stabilization techniques–the Characteristic-Based Split (CBS) and the Algebraic-Flux Correction (AFC) method–is employed to solve the equations numerically in space and time. The nodes of the computational mesh are updated together with the flow of the phase described in the Lagrangian description. The computational mesh is updated by applying techniques used in the so-called Particle Finite Element Method (PFEM), characterized by regenerating the mesh in each computational step according to the updated nodal positions while the current boundary of the domain is identified using α -shape method. The performance of the method is demonstrated by means of three 2D and 3D examples, including a mixing process of two fluids in a stirred tank, a free surface flow, a 3D two-phase channel flow, a phase separation problem and the flow of two immiscible fluids.