A Semi-Lagrangian Finite Element Method for Two-Phase Flows
Congress: JEM
ABSTRACT:
This work aims to present a computational approach to study two-phase flows using direct numerical simulation. The flows are modeled by the two-dimensional 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 in the temporal domain. A static unstructured triangular mesh is defined in the whole spatial domain. In order to satisfy the Ladyzhenskaya–Babuška–Brezzi condition, the mini and the quadratic elements are used, with pressure and velocity fields being calculated on different sets of the triangular mesh points. The interface is modeled by an adaptive moving one-dimensional mesh, according to a front- tracking method, in which connected marker points are moved with the imposed velocity of the triangular mesh. The interfacial tension is calculated using the interface curvature and a Heaviside function gradient, and included in the Navier-Stokes equations as a volume force. In order to stabilize the simulation results, a smooth transition between fluid properties is defined on the interface region. Several benchmark tests, such as the rising bubble and the oscillating drop, have been carried out to validate the proposed approach and the obtained results have matched analytical solutions and results found in literature. Therefore, the presented approach is validated to provide an accurate description of diverse two-phase flow phenomena.