The second gradient theory: a tool for the direct numerical simulation of liquid-vapor flows with phase-change

In several numerical methods dedicated to the direct numerical simulation o f two-phase flows, the concept of a continuous enlarged interfacial zone is used. In this communication, it is shown that for liquid-vapor systems, it is possible to use this concept in a thermodynamic coherent way. Indeed, i f it is considered that the energy of the system depends on the density gra dient, this theory being called the Van der Waals or Cahn-Hilliard or more generally the second gradient theory, then it is possible to derive the equ ations that characterize the fluid motion within a 3-D liquid-vapor interfa cial zone. Modifying the thermodynamic behavior of the fluid, it is shown t hat it is possible to increase the thickness of an interface, so that it ca n be captured by a 'standard' mesh without changing the surface tension nor loosing the thermodynamic coherence of the model. Several examples of appl ication show that this method can be applied to study various physical prob lems, including contact line phenomena. (C) 2001 Elsevier Science B.V. All rights reserved.