A conservative phase field method for solving incompressible two-phase flows

In this paper a conservative phase-field method based on the work of Sun and Beckermann [Y. Sun, C. Beckermann, Sharp interface tracking using the phase-field equation, J. Comput. Phys. 220 (2007) 626–653] for solving the two- and three-dimensional two-phase incompressible Navier–Stokes equations is proposed. The present method can preserve the total mass as the Cahn–Hilliard equation, but the calculation and implementation are much simpler than that. The dispersion-relation-preserving schemes are utilized for the advection terms while the Helmholtz smoother is applied to compute the surface-tension force term. To verify the proposed method, several benchmarks are examined and shown to have good agreements with previous results. It also shows that the satisfactions of mass conservations are guaranteed.