High-fidelity and reduced-order modelling of viscoelastic filaments

Accurate and stable simulations of the hyperbolic constitutive equations describing viscoelastic flows remain challenging, especially for flows containing complex topological transitions such as spray formation and fragmentation. The development of singularities in the solution to the constitutive equations at high strain rates or large polymer relaxation times is known to lead to numerical instabilities that challenge convergence. Here, we consider axisymmetric simulations of an impulsively-started low-speed viscoelastic jet exiting a nozzle using the open-source Eulerian code Basilisk. We identify the distinct flow regimes characterizing the thinning and the “pinch-off singularities” in the viscoelastic filament, revealing the effects of the jet speed and the polymeric extensibility. We also perform three-dimensional simulations at higher injection flowrates, exploiting the capabilities of adaptive grid refinement to capture the interface accurately within a volume-of-fluid framework. In addition, a less expensive frame-invariant data-driven rheological model is employed and compared to DNS. We demonstrate that key dynamical features of the stretching viscoelastic filaments can be captured by transporting the trace of the conformation tensor and reconstructing the full constitutive model algebraically using symbolic regression.