Non-isothermal two-phase flow with a diffuse-interface model

In this paper a previously developed diffuse-interface method for numerical simulation of isothermal two-phase flow of a single component is extended to non-isothermal situations. Since no artificial spreading of the interface is applied and no local grid refinement is used, the fluid should be close to its critical point to have an interfacial thickness not too small compared to the size of the computational domain. The use of a non-monotonic Van der Waals equation of state in the vicinity of the critical point causes elliptical behavior of the system of governing equations in part of the phase diagram. A linear stability analysis shows that the rate at which small perturbations grow is reduced with respect to the isothermal case. By adopting a Total Variation Diminishing time-integration scheme, a stable solution method is obtained. One- and two-dimensional simulations are performed to test the applicability and accuracy of the method. The dynamics of the head-on collision of two drops is studied for various combinations of Weber and Prandtl numbers, with particular attention to the effect of the temperature distribution.