Physically bounded material interpolation for rheologically accurate multiphase flows

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 computational stability. We propose a hyperbolic tangent-based interpolation scheme that addresses these limitations while preserving computational efficiency. The scheme ensures that material properties remain bounded within physically consistent ranges, even if the phase field variable itself overshoots or undershoots, thereby suppressing nonphysical deviations that destabilize numerical simulations. Moreover, the proposed interpolation scheme provides a sharply defined transition for both thermophysical and rheological properties, preserving distinct phase characteristics and preventing cross-phase contamination. This capability is particularly valuable for heterogeneous systems such as viscoelastic–Newtonian multiphase flows, without the numerical smearing and spurious stress invasion often encountered in conventional interpolation schemes. Through numerical experiments with adaptive mesh refinement, we demonstrate that our approach achieves accuracy comparable to conventional approaches while exhibiting superior robustness. The key advantages of the scheme are (1) straightforward integration by replacing the interpolation scheme, (2) distinct interfaces across all thermophysical and rheological properties, and (3) inherent boundedness of material properties. These features highlight the proposed method broadly applicable to challenging multiphase problems involving fluids with highly disparate physical properties.