Generalized Navier Boundary Condition and Geometric Conservation Law for surface tension

Jean-Frédéric Gerbeau 1 Tony Lelièvre 2
1 REO - Numerical simulation of biological flows
LJLL - Laboratoire Jacques-Louis Lions, Inria Paris-Rocquencourt, UPMC - Université Pierre et Marie Curie - Paris 6
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.
Document type :
Reports
Complete list of metadatas

Cited literature [23 references]  Display  Hide  Download

https://hal.inria.fr/inria-00285206
Contributor : Rapport de Recherche Inria <>
Submitted on : Monday, June 9, 2008 - 10:31:40 AM
Last modification on : Wednesday, May 15, 2019 - 3:35:44 AM
Long-term archiving on : Friday, November 25, 2016 - 9:05:57 PM

Files

RR-6551.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : inria-00285206, version 2

Citation

Jean-Frédéric Gerbeau, Tony Lelièvre. Generalized Navier Boundary Condition and Geometric Conservation Law for surface tension. [Research Report] RR-6551, INRIA. 2008, pp.32. ⟨inria-00285206v2⟩

Share

Metrics

Record views

504

Files downloads

989