Computation of Deformable Interface Two-Phase Flows:A Semi-Lagrangian Finite Element Approach

This work aims at presenting a new computational approach to study two and three dimensional two-phase flows and two dimen-sional coalescence phenomenon using direct numerical simulation. The flows are modeled by the incompressible Navier–Stokesequations, which are approximated by the finite element method. The Galerkin formulation is used to discretize the Navier–Stokesequations in the spatial domain and the semi-Lagrangian method is used to discretize the material derivative. In order to satisfy theLadyzhenskaya–Babuška–Brezzi condition, high-order stable pair of elements are used, with pressure and velocity fields beingcalculated on different degrees of freedom in the unstructured mesh nodes. The interface is modeled by an unfitted adaptive mov-ing mesh, where interface nodes are tracked in a Lagrangian fashion and moved with the velocity solution of the fluid motionequations. The surface tension is computed using the interface curvature and the gradient of a Heaviside function, and added inthe momentum equations as a body force. In order to avoid undesired spurious modes at the interface due to high property ratios,a smooth transition between fluid properties is defined on the interface region. Several benchmark tests have been carried out tovalidate the proposed approach, and the obtained results have demonstrated agreement with analytical solutions and numericalresults reported in the literature. A coalescence model is also proposed based on geometric criteria and results show interestingdynamics.