Simulating interfacial deformation by arbitrary Lagrangian–Eulerian approach

Abstract

One of chief advantages of using the simplified arbitrary Lagrangian–Eulerian (Simplified ALE) method is that the time dependent interfacial problem of fluid layers, which is often treated as moving boundary problem, can be simulated with a technique of the rezoning and remeshing involved in the method. In this text, a numerical technique based on the simplified arbitrary Lagrangian–Eulerian method for simulating the behavior of time-dependent interfacial stratified fluids of viscoelastic nature is described to understand the numerical method. Particularly in dealing with viscoelastic fluid flow of an integral-type constitutive equation, the strain history is obtained by the memory integration method in a moving Lagrangian grid. Excess distortion of mesh elements due to fluid straining is overcome by the use of an arbitrary Lagrangian–Eulerian treatment of the continuous mesh rezoning. Specially in this text the scheme is applied to simulate an interfacial deformation of stratified fluids at model Y-junctions of two laminar layers. From the results of a benchmark calculation, the present scheme is found to show good agreement with a previous numerical work of the finite element method and predict some important flow phenomena that can appear in the flow geometry of viscoelastic fluids in experiments.