GALUSINSKI, Cedric; VIGNEAUX, Paul

doi:10.1016/j.jcp.2008.02.023

Métadonnées

Licence d’utilisation du document

GALUSINSKI, Cedric
Institut de Mathématiques de Toulon - EA 2134 [IMATH]

VIGNEAUX, Paul
Institut de Mathématiques de Bordeaux [IMB]
Laboratoire de Mathématiques [LAMA]
Numerical Medicine [NUMED]

Langue

Article de revue

Ce document a été publié dans

Journal of Computational Physics. 2008-06-01, vol. 227, n° 12, p. 6140-6164

Elsevier

Résumé en anglais

Models for incompressible immiscible bifluid flows with surface tension are here considered. Since Brackbill, Kothe and Zemach (J. Comput. Phys. 100, pp 335-354, 1992) introduced the Continuum Surface Force (CSF) method, many methods involved in interface tracking or capturing are based on this reference work. Particularly, the surface tension term is discretized explicitly and therefore, a stability condition is induced on the computational time step. This constraint on the time step allows the containment of the amplification of capillary waves along the interface and puts more emphasis on the terms linked with the density in the Navier-Stokes equation (i. e. unsteady and inertia terms) rather than on the viscous terms. Indeed, the viscosity does not appear, as a parameter, in this stability condition. We propose a new stability condition which takes into account all fluid characteristics (density and viscosity) and for which we present a theoretical estimation. We detail the analysis which is based on a perturbation study - with capillary wave - for which we use energy estimate on the induced perturbed velocity. We validate our analysis and algorithms with numerical simulations of microfluidic flows using a Level Set method, namely the exploration of different mixing dynamics inside microdroplets.< Réduire

Mots clés en anglais

surface tension

curvature

stability condition

bifluid flows

incompressible Navier-Stokes

level set

cartesian finite-volumes

microfluidics

droplets

DOI

http://dx.doi.org/10.1016/j.jcp.2008.02.023

Project ANR

SCAN (Smart Chips for Analysis) - ANR-06-NANO-0048

Origine

Importé de hal

Unités de recherche

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251