A sharp computational method for simulating multiphase viscoelastic flows

doi:10.1016/j.jnnfm.2025.105559

A sharp computational method for simulating multiphase viscoelastic flows

2026-01-02

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Joseph Vincent Giliberto *

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Olivier Desjardins

DOI：10.1016/j.jnnfm.2025.105559

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Viscoelastic constitutive equations often model the elastic stress field through the use of an elastic dumbbell model that utilizes a conformation tensor to represent the average polymer configuration in the flow field. In a liquid-gas flow environment, the conformation tensor is a discontinuous quantity that only exists in the liquid phase. This discontinuity often presents numerical challenges that can be tackled through the use of very fine meshes at the interface to ensure the stress profile is accurately captured. In contrast, this work presents a hybrid advection scheme for the discontinuous conformation tensor field that uses a semi-Lagrangian geometric flux-based scheme in the direct vicinity of the liquid-gas interface and a MUSCL scheme in the bulk of the liquid, away from the interface. This hybrid method is found to be exactly conservative and bounded, and prevents any leakage of data across the liquid-gas interface. Verification and validation of this approach is done using the case of a gas bubble rising in a viscoelastic liquid. Results of the convergence study show that the hybrid scheme is able to converge to experimental results with 32 cells across the initial diameter of the bubble, which is one-third the resolution used in other computational studies comparing against experiments. The hybrid advection scheme is then applied to the case of a viscoelastic droplet deforming in homogeneous isotropic turbulence to investigate the influence of elastic stresses on droplet morphology. Results indicate that increasing viscoelastic stresses within the droplet significantly alters its deformation dynamics. At the moderate elastic stress levels tested, the droplet forms elongated liquid filaments delaying break-up for a longer duration. As viscoelasticity is further increased, deformation is progressively suppressed, ultimately stabilizing the droplet’s shape and preventing fragmentation.

A sharp computational method for simulating multiphase viscoelastic flows

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