Arbitrary Lagrangian-Eulerian FEM for Two-Phase Flows: New Methods

Abstract

This chapter presents a series of new methods used in the numerical modeling of two-phase flows based on the arbitrary Lagrangian-Eulerian (ALE) formulation and the finite element method (FEM). Theoretical considerations concerning the imposition of periodic boundary conditions through a variationally consistent framework, as well as their implementation techniques for a class of 3D two-phase flows are provided. Mesh design tools, pre-processing tasks, adaptive refinement, gradient-based finite element spaces and their applicability in the modeling of bubble flows are introduced. Cases highlighting single and multiple bubbles arranged as slug and annular flow patterns are idealized, as well as pressure gradient- and gravity-driven flows. Supplementary comments point out ongoing and future challenges relating to the numerical development of ALE-FEM-based strategies.