An energy diminishing arbitrary Lagrangian–Eulerian finite element method for two-phase Navier–Stokes flow

Abstract

A linearized fully discrete arbitrary Lagrangian–Eulerian finite element method is proposed for solving the two-phase Navier–Stokes flow system and to preserve the energy-diminishing structure of the system at the discrete level, by taking account of the kinetic, potential and surface energy. Two benchmark problems of rising bubbles in fluids in both two and three dimensions are presented to illustrate the convergence and performance of the proposed method.