Two-Step Semi-Lagrangian Integration for ALE/FEM Two-Phase Flows

Abstract

In this paper we propose a two-step semi-Lagrangian-finite element scheme to track particle trajectories traveling amidst incompressible two-phase flows in moving mesh situations. The procedure is based on a dual backward-in-time integration that embodies the mesh velocity information. Firstly, a search for departure points is carried out by using an Adams-Bashforth estimator; secondly, a correction of the departure points is done through interpolation. Two-phase flow simulations for usual configurations (e.g. rising bubble flow, horizontal bubbly flow) are conducted to compare the performance of the new integrator against single-step approximations. Error analyses and mesh convergence tests are presented to highlight the superior conservativeness of the current scheme in space and time.