A compressible flow model with capillary effects

A quasi-conservative formulation for compressible flows with interfaces including both capillary and viscous effects is developed. The model involves: (i) acoustic and convective transport; (ii) surface tension effects introduced as an extension of the CSF method (Brackbill et al.) to compressible flows; (iii) viscous effects. The interfaces are considered as diffused zones. Every point of the flow is correctly described thanks to a mixture equation of state based on energy conservation and pressure equilibrium. The model is thus valid in each pure fluid as well as at interfaces. A Godunov type method, that enables interface capturing, is developed and used whatever the mesh point. Numerical tests are performed over a wide range of physical situations involving surface tension, compressibility, gravity, viscosity and large density ratios. Tests involving break-up and coalescence are considered to show the ability of the method to deal with dynamic appearance and disappearance of interfaces in an Eulerian framework. (c) 2005 Elsevier Inc. All rights reserved.