A novel profile-preserving Phase-Field method to model multiphase flows

The Phase-Field methods, also known as the Diffuse-Interface methods, have been popularly used to model multiphase flows. The order parameters, governed by the Phase-Field equation, not only serve as phase indicators but also are related to computing the density of the fluid mixture and the surface tension force. After implementing the consistent and conservative volume distribution algorithm, a novel Phase-Field equation is developed, aiming to (i) conserve the mass of each phase, (ii) maintain the interface thickness, and (iii) preserve the equilibrium profile across phase interfaces. These properties are beneficial to avoid excessive numerical diffusion that keeps thickening the interfaces, to reduce distortion of the interfacial profile due to flow advection, and to improve the accuracy of computing the buoyancy and surface tension forces. Then, this novel Phase-Field equation is coupled to the flow dynamics consistently, and canonical problems are performed to demonstrate its effectiveness.