Generalized Navier Boundary Condition and Geometric Conservation Law for surface tension

TL;DR

This paper develops a framework for two-fluid flow problems with moving contact lines, introducing generalized boundary conditions and an extended geometric conservation law to improve stability and accuracy in numerical simulations involving surface tension.

Contribution

It introduces the Generalized Navier Boundary Conditions and extends the Geometry Conservation Law to moving surfaces, enhancing stability analysis in two-fluid flow simulations.

Findings

Stable numerical schemes for two-fluid flows with moving contact lines.

Effective handling of surface tension effects in ALE framework.

Balance between efficiency, stability, and artificial diffusion achieved.

Abstract

We consider two-fluid flow problems in an Arbitrary Lagrangian Eulerian (ALE) framework. The purpose of this work is twofold. First, we address the problem of the moving contact line, namely the line common to the two fluids and the wall. Second, we perform a stability analysis in the energy norm for various numerical schemes, taking into account the gravity and surface tension effects. The problem of the moving contact line is treated with the so-called Generalized Navier Boundary Conditions. Owing to these boundary conditions, it is possible to circumvent the incompatibility between the classical no-slip boundary condition and the fact that the contact line of the interface on the wall is actually moving. The energy stability analysis is based in particular on an extension of the Geometry Conservation Law (GCL) concept to the case of moving surfaces. This extension is useful to study the contribution of the surface tension. The theoretical and computational results presented in this paper allow us to propose a strategy which offers a good compromise between efficiency, stability and artificial diffusion.