Obtain converged simulations at higher Deborah numbers

Obtain converged finite-element simulation results for radial Oldroyd-B flow between parallel plates at Deborah numbers above $De=0.46$ ($Wi=11.5$) when the polymer-to-total viscosity ratio is $ ilde{eta}=0.05$, using a log-conformation formulation and suitable viscoelastic-flow solvers.

Background

The paper develops a lubrication-based ultra-dilute theory for the pressure drop and conformation tensor in radial Oldroyd-B flow at order-one Deborah numbers, and validates the theory against axisymmetric finite-element simulations. The numerical simulations use COMSOL Multiphysics and provide inlet conformation-tensor data required by the semi-analytical theory. However, numerical convergence becomes difficult as the Deborah number increases, limiting validation of the theory at higher elasticity. The authors identify log-conformation methods and alternative solvers as potential means of extending the accessible Deborah-number range.

References

Unfortunately, in COMSOL Multiphysics, we are currently unable to obtain converged finite-element simulation results beyond $De=0.46$ ($Wi=11.5$) for $\tilde{\beta}=0.05$. Therefore, as a future research direction, it would be interesting to obtain numerical results at higher Deborah numbers using the log-conformation formulation~\citep{fattal2004constitutive}, as implemented, for example, within the finite-volume software OpenFOAM~\citep{jasak2007openfoam}, coupled with the viscoelastic flow solver RheoTool~\citep{pimenta2017stabilization}, similar to recent studies by~\citet{mahapatra2025viscoelastic} and~\citet{kedem2026viscoelastic}.

— Radial flow of an Oldroyd-B fluid: theoretical and simulation results in the ultra-dilute limit  (2609.36831 - Lottem et al., 29 Sep 2026) in Section 6, Concluding remarks