Arbitrary Lagrangian-Eulerian Method for Two-Phase Flows

Abstract

A modern numerical method is described to study two-phase flows for single and multiple bubbles in complex geometries. The fluid flow equations are developed in 3-dimensions based on the Arbitrary Lagrangian-Eulerian formulation (ALE) and the Finite Element Method (FEM), creating a new two-phase method with an improved model for the liquid-gas interface. A successful adaptive mesh update procedure is also proposed for effective management of the mesh at the two-phase interface to remove, add and repair surface elements, since the computational mesh nodes move according to the flow. The Lagrangian description explicitly defines the two-phase interface position by a set of interconnected nodes which ensures a sharp representation of the boundary, including the role of the surface tension. The new methodology proposed for computing the curvature leads to accurate results with moderate programming effort and computational cost, which can be also applied to different methods with explicitly description of the interface.