Systematic comparison of inverse Langevin function approximations in stochastic dumbbell dynamics

Finite extensibility strongly influences the nonlinear dynamics of dilute polymer solutions, yet its representation in stochastic dumbbell models typically relies on approximate forms of the inverse Langevin function. Here, we systematically examine how commonly used inverse Langevin function approximations affect both the model predictions and numerical behavior of stochastic dumbbell models. Using the Brownian Configuration Field formulation, we directly integrate the full stochastic equations for finitely extensible dumbbells and compare three spring-force representations: the classical Finitely Extensible Nonlinear Elastic (FENE) model and two Padé-based approximations due to Cohen and Rickaby-Scott. Model predictions are assessed in large-amplitude oscillatory shear, steady uniaxial extensional, and capillary thinning flows for different parameter values. The results show that differences emerge when chains remain at moderate extension, whereas weakly deformed chains and chains rapidly driven to near-full extension exhibit model-independent behavior. In these transitional regimes, the FENE model consistently predicts lower stretch and stress levels than the Padé-based approximations, with discrepancies increasing for highly extensible chains. Analysis of the governing equations further demonstrates that the choice of approximation controls the stiffness of the stochastic dynamics near full extension, directly impacting numerical stability in coupled flow simulations. These results indicate that the choice of inverse Langevin approximation can measurably affect both model predictions and numerical robustness in stochastic simulations of nonlinear viscoelastic flows.