On a finite element formulation for incompressible Newtonian fluid flows on moving domains in the presence of surface tension

Abstract

SUMMARYThis work is concerned with the numerical modelling of incompressible Newtonian uid ows on moving domains in the presence of surface tension. The solution procedure presented is based on the stabilized equal order mixed velocity-pressure ÿnite element formulation of the incompressible Navier-Stokes equations, which is adapted to a moving domain by means of an arbitrary Lagrangian-Eulerian (ALE) technique. The accurate and very robust integration in time is achieved by employing the generalizedmethod. The surface tension boundary condition is rephrased appropriately within the framework of linear ÿnite elements. The solution procedure is veriÿed by comparing numerical solutions with the corresponding analytical solutions and experimental data. The overall solution procedure proves to be accurate, robust and e cient. It allows the simulation of extensive deformation of the uid domain without remeshing.

A Fully Implicit Computational Strategy for Strongly Coupled Fluid–Solid Interaction

“…The variational form (20) consists of the standard Galerkin terms summarised in G Gal , to which a stabilisation term G stab of the momentum equation has been added. In order to simplify the notation in the remainder of this section, which is dedicated to the detailed presentation of G Gal and G stab , the coupling of (20) with the deformation of the solid structure is not explicitly included.…”

“…Such techniques have become standard in Eulerian finite element formulations and have been applied to various problems arising in fluid mechanics (see e.g. [4][5][6][7][16][17][18][19][20][21]). A review of a variety of stabilisation techniques may be found in [22].…”

On finite element modelling of surface tension Variational formulation and applications – Part I: Quasistatic problems

“…This finding significantly simplified the problem at hand. The Lagrangian finite element simulations incorporating surface tracking technique with boundary fitted meshes are described in [9,24] for 2-D applications while in [25][26][27] the authors focus on axisymmetric problems. In recent years several authors have also described simulations of free surface flows problem with surface tension in three dimensions [28,29].…”

Towards numerical prototyping of labs-on-chip: modeling for integrated microfluidic devices

“…This technique tracks a series of surface markers placed along the interface, which are advected to their new position at each time step based on the previous time step's computed interfacial velocity. Arbitrary Lagrangian-Eulerian (ALE) methods are also commonly used when surface tension effects are important (see Donea et al (2004) for an overview and Dettmer et al (2003) for an example). As the name implies, ALE methods exploit the advantages of both Lagrangian and Eulerian frames of reference to simplify the computation and maintain a high mesh quality (versus a purely Lagrangian approach) as the interface moves.…”