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

## Palavras-chave:

Two-phase flows, coalescence, Finite Element Method, semi-Lagrangian, unstructured mesh## Resumo

This work aims at presenting a computational approach to study two-phase flows and the coalescence

phenomenon using direct numerical simulation. The flows are modeled by the incompressible Navier-Stokes

equations, which are approximated by the Finite Element Method. The Galerkin formulation is used to discretize

the Navier-Stokes equations in the spatial domain and the semi-Lagrangian method is used to discretize the material

derivative backward in time. In order to satisfy the Ladyzhenskaya–Babuska–Brezzi condition, high-order pair of ˇ

elements are used, with pressure and velocity fields being calculated on different sets of the unstructured mesh

nodes. The interface is modeled by an uncoupled adaptive moving mesh, where interface nodes are tracked in

a Lagrangian fashion and moved with the velocity solution of the motion equations. The interface tension is

computed using the interface curvature and the gradient of a Heaviside function, and added in the momentum

equations as a volume force. In order to stabilize the simulation, a smooth transition between fluid properties is

defined on the interface region. Several benchmark tests have been carried out to validate the proposed approach,

and the obtained results have demonstrated agreement with analytical solutions and results reported in the literature.

A coalescence modeling is also proposed considering geometric parameters and results show interesting dynamics.