Variational solutions for the discrete nonlinear Schrödinger equation Original Research Article

For interface-tracking simulation of two-phase flows with a high density ratio, we propose a computational method, NS–PFM, combining Navier–Stokes (NS) equations with phase-field model (PFM) based on the free energy theory. Through the numerical simulations, it was confirmed that (1) the volume flux derived from chemical potential gradient in the Cahn–Hilliard equation of PFM plays an important role in advection and reconstruction of interface, and (2) the NS–PFM gives good predictions for the motions of immiscible, incompressible, isothermal two-phase fluid, such as air–water system, without using conventional interface-tracking techniques.