Implementation of the Accurate Conservative Phase Field Method for Two-Phase Incompressible Flows in a Finite Volume Framework

The phase field method provides a simple mass conserving method for solving two-phase immiscible-incompressible Navier–Stokes Equations. The relative ease in implementing this method compared to other interface reconstruction methods, coupled with its conservativeness and boundedness makes it an attractive alternative. We implement the method in a parallel structured multi-block generalized coordinate finite volume solver using a collocated grid arrangement within the framework of the fractional step method. The discretization uses a second-order central difference method for both the Navier–Stokes and the phase field equations. A TVD-based averaging technique is used for calculating density at cell faces in the pressure correction step to handle high-density ratios. The simulation framework is verified in standard test cases: Zalesak Disk, a droplet in shear flow, Solitary Wave Run-up, Rayleigh Taylor Instability, and the Dam Break Problem. A second-order rate of convergence and excellent phase volume conservation is observed.