Generalized Navier boundary condition and geometric conservation law for surface tension
We consider two-fluid flow problems in an arbitrary LagrangianEulerian (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 condition (GNBC). Owing to these boundary conditions, it is possible to circumvent the incompatibility between the classical no-slip boundary conditions 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 geometric 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.
generalized navier boundary condition geometric conservation law energy stability analysis arbitrary lagrangianeulerian method moving contact line problem