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.