3D Arbitrary Lagrangian–Eulerian approach for multiphase flow with an efficient sharp interface tracking

Multiphase flow phenomena present a significant challenge due to their highly variable nature and the interaction between multiple phases, which are characterised by different temporal and spatial scales. In particular, the interfaces between fluids require accurate modelling as they may undergo complex evolution and, eventually, topological changes. This paper proposes an advanced numerical method for simulating three-dimensional, immiscible, two-phase flows, where the interface surface is well-defined and surface tension is neglected, in order to focus on the discontinuity of physical properties across the interface. The incompressible Navier-Stokes equations are solved using a Finite Element Arbitrary Lagrangian-Eulerian framework with a one-fluid formulation. The interface is tracked using Lagrangian nodes, and physical properties are assigned element-wise, assuming a sharp interface between the two distinct fluids. To capture pressure jump discontinuities, an auxiliary pressure variable is introduced, which is continuous throughout the entire domain. The actual pressure field is then reconstructed a posteriori by evaluating the boundary conditions at the interface. Finally, a remeshing algorithm based on connectivity manipulation and a local refinement procedure is implemented to reduce element distortion in the fluid mesh, thereby increasing the accuracy of the solution. Several analytical and numerical benchmarks are presented to evaluate the accuracy and reliability of the proposed numerical scheme in handling large interface deformations and strong pressure jumps, without requiring extremely refined meshes in the vicinity of the two-fluid interface.