Modeling two-phase flow in converging channels using deformable and fixed methods to describe the interface

Several methods have been developed in recent years for the solution of free surface flows. These methods can be divided into two main categories: moving grid methods (also known as Lagrangian or interface tracking methods), and fixed grid methods (also known as Eulerian or interface capturing methods). In the first approach the mesh has grid points on the interface and each computational cell contains the same fluid phase. The principal advantages are the simplification of the imposition of boundary conditions on the interface and the high accuracy of the description of the interface configuration and curvature, therefore, this method should be used to solve problems in which capillary forces are important. In the second approach, the boundary of a two-fluid interface is implicitly “captured” solving a scalar equation – pseudo-concentration method (Thompson, 1986) – on the entire stationary grid, i.e. there is a predefined grid that does not move with the interface. The interface may undergo large deformations, and it is relatively straightforward to handle multiple interfaces. However, the high accuracy of the description of the interface configuration is lost. In this paper, the performance of both approaches is compared by analyzing the interface between two Newtonian liquids flowing in two convergent channels that merge into a single channel. The effect of the flow rate of each liquid and viscosity ratio are analyzed. The differential equations that describe the flow are solved by Galerkin/FEM.