Robust Material Property Interpolation for Diffuse Interface Methods

Abstract

The phase field method is widely employed for predicting multiphase flows; however, numerical artifacts from bulk diffusion often lead to unphysical material properties and compromise stability. Weintroduce a robust interpolation scheme for material properties that addresses these limitations while preserving computational efficiency. Our method employs a hyperbolic tangent interpola tion function that strictly guarantees material properties are determined by the physical bounds of the two bulk phases, even if the phase field variable itself overshoots or undershoots. This eliminates fictitious phases and ensures physically consistent material properties, when combined with appropriate mesh refinement. The implementation establishes a numerical Gibbs dividing surface that mirrors thermodynamic principles, enabling accurate representation of abrupt property transitions between phases. This proves particularly valuable for complex rheological systems such as viscoelastic-Newtonian fluid interactions, where diffuse interfaces with large property contrasts typically cause undesirable invasion of phase properties that impacts prediction accuracy. Through numerical experiments with adaptive mesh refinement, we demonstrate that our approach preserves distinct material characteristics in each phase, preventing elastic stress contamination in Newtonian regions. The proposed method enhances both stability and accuracy of multiphase computations without significant modification of the phase field method, making it suitable for challenging problems involving interfaces between fluids with disparate physical properties.

Keywords: Multiphase flow, Phase field method, Hyperbolic tangent interpolation scheme, Quasicompressibility, Viscoelasticity, Adaptive mesh refinement method