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In this paper, we introduce an interfacial profile-preserving approach forphase field modeling for simulating incompressible two-phase flows. While theadvective Cahn-Hilliard equation effectively captures the topological evolutionof complex interfacial structures, it tends to displace the fluid interfacefrom its equilibrium state, impacting simulation accuracy. To tackle thischallenge, we present an interfacial profile-preserving formulation that relieson a phase-field-related signed distance function, rather than the phase fieldfunction itself. It is solved iteratively to restore the equilibrium interfaceprofile after each time step. This approach effectively minimizesdiscretization errors and enhances mass conservation accuracy for each phase.Our formulation is discretized using a second-order Total Variation Diminishing(TVD) Runge-Kutta method within iterations and a finite volume scheme inspatial discretization. We quantitatively compare our presentprofile-preserving method with the original method in terms of accuracy andconvergence rate through simulations of a deforming drop in a single vortex anda rising bubble in quiescent fluid, and further validate the applicabilitythrough simulations of a two-dimensional contracting liquid filament, a dropimpacting a deep liquid pool, and three-dimensional drop deformation in shearflow. Our results exhibit good agreement with analytical solutions, priornumerical results, and experimental data, demonstrating the effectiveness andaccuracy of our proposed approach.

An Interfacial Profile-Preserving Approach for Phase Field Modeling of Incompressible Two-Phase Flows