An interfacial profile-preserving approach for phase field modeling of incompressible two-phase flows.

The Phase Field Method stands as a promising technique for modeling complex two-phase and multi-phase flow systems, with the advective Cahn–Hilliard equation adept at capturing the evolution of intricate interfacial structures. However, achieving simulation accuracy necessitates the preservation of the diffuse interface profile, which is often challenged by the convection term within the Cahn–Hilliard equation, leading to deviations from the equilibrium interface state. To address this challenge, we introduce an innovative approach aimed at iteratively restoring the equilibrium interface profile after each time step. This method combines a level-set profile-corrected equation with an algebraic relation between the phase field and the signed distance function, resulting in a preservation equation that relies on the phase-field-related signed distance function rather than the phase field function itself. Quantitative computational tests affirm the effectiveness of this approach in minimizing discretization errors, reducing dependence on the numerical P e ́ clet number, and improving mass conservation accuracy for each phase, all while reducing computational time by approximately 20-fold due to the coarser grid used. Validation through simulations across various scenarios demonstrates the approach's reliability, with results closely aligning with analytical solutions, prior numerical findings, and experimental data, thereby underscoring the efficiency and precision of our proposed approach. [Display omitted] • Profile-preserving formulation for phase field methods in simulating two-phase flows. • Reduced computational cost and improved mass conservation on a coarser grid. • Lower sensitivity to numerical Péclet numbers, minimal computational expense. • Rigorous validation in surface tension-dominant scenarios affirms reliability. [ABSTRACT FROM AUTHOR]