Fluid simulation is a central topic in computer graphics, encompassing a wide range of methodologies for modeling Newtonian, non-Newtonian, and viscoelastic behaviors across both single-phase and multiphase settings. Existing single-phase frameworks have achieved high visual fidelity, yet multiphase simulations remain limited in accurately capturing complex phase interactions, particularly under high-viscosity-ratio or viscoelastic conditions. To address these challenges, we develop a unified multiphase viscoelastic formulation capable of handling diverse fluid types-including Newtonian, shear-dependent non-Newtonian, and viscoelastic flows-within a single consistent framework. The formulation extends mixture-model approaches through a multi-mode conformation tensor representation, which enhances numerical stability via phase-level stress corrections and efficiently captures a broad spectrum of rheological behaviors. Compared with existing techniques, our framework achieves improved momentum-mass consistency and numerical stability, maintaining physically plausible results across wide viscosity ranges, advancing the state of the art in multiphase viscoelastic fluid simulation.
Shen et al. (Thu,) studied this question.