Far field boundary conditions for incompressible flows computation

Many far field boundary conditions are proposed in the literature to solve Navier-Stokes equations. It is necessary to distinguish the streamwise or outlet boundary conditions and the spanwise boundary conditions. In the first case the flow crosses the artificial frontier and it is required to avoid reflections that can change significantly the flow. In the second case the Navier-slip boundary condition is often used but if the frontier is not far enough the boundary is both inlet and outlet. Thus the Navier-slip boundary condition is not well suited as it imposes no flux through the frontier. The aim of this work is to compare some well-known boundary conditions, to quantify to which extend the artificial frontier can be close to the bodies in two- and three-dimensions and to take into account the flow rate through the spanwise directions.     

Front‐tracking by the level‐set and the volume penalization methods in a two‐phase microfluidic network

Two‐phase immiscible fluids in a two‐dimensional micro‐channels network are considered. The incompressible Stokes equations are used to describe the Newtonian fluid flow, while the Oldroyd‐B rheological model is used to capture the viscoelastic behavior. In order to perform numerical simulations in a complex geometry like a micro‐channels network, the volume penalization method is implemented. To follow the interface between the two fluids, the level‐set method is used, and the dynamics of the contact line is modeled by Cox law. Numerical results show the ability of the method to simulate two‐phase flows and to follow properly the contact line between the two immiscible fluids. Finally, simulations with realistic parameters are performed to show the difference when a Newtonian fluid is pushed by a viscoelastic fluid instead of a Newtonian one. Copyright © 2015 John Wiley & Sons, Ltd.