Recent studies demonstrate that flow induced non-uniformities of concentration can trigger shear banding in the flow of certain viscoelastic fluids. These studies show that the driving mechanisms for such shear banding are related to the coupling of the polymer stresses to an inhomogeneous concentration profile. The Rolie-Poly (RP) viscoelastic constitutive model has been used in such studies since it has been comprehensively subjected to extensive experimental validation with regards to shear banding and has the demonstrated ability to accurately express the rheology of polymer solutions for a wide range of strain rates. The primary aim of this work is to develop an efficient computational methodology that could be used to accurately simulate the flow of complex fluids governed by the Rolie-Poly constitutive equation. The development of such a computational platform is crucially important for the purposes of our follow up studies on the computational analysis of shear banding phenomena by coupling polymer stress with inhomogeneous concentration profile. Our numerical algorithms will be based on the finite volume method (FVM) and will be implemented on the open source software package OpenFOAM®. In this paper, we will present both validation results as well as new benchmark results from our FVM based OpenFOAM®numerical solver for flow of fluids governed by the Rolie-Poly constitutive model. We use two well-known benchmark problems, the lid-driven cavity flow and the 4:1 planar contraction flow problems. In order to stabilize the numerical algorithm at high Weissenberg numbers, we employ either of two stabilization techniques; the Discrete Elastic Viscous Stress Splitting (DEVSS) technique as well as the Log-Conformation Reformulation (LCR) methodology. Validation of our results is done by comparing our (stabilized) numerical results, against data from existing literature. The numerical results obtained for the contraction flow using the LCR stabilization approach are in good agreement with the existing literature for a wider range of Weissenberg numbers. The DEVSS method shows a good agreement only for lower Weissenberg numbers. For the lid-driven cavity flow, good agreement with the existing literature is observed for low Weissenberg numbers using either of the two stabilization techniques.

The flow of viscoelastic fluids may, under certain conditions, exhibit shear-banding characteristics that result from their susceptibility to unusual flow instabilities. In this work, we explore both the existing shear banding mechanisms in the literature, namely; constitutive instabilities and flow-induced inhomogeneities. Shear banding due to constitutive instabilities is modelled via either the Johnson–Segalman or the Giesekus constitutive models. Shear banding due to flow-induced inhomogeneities is modelled via the Rolie–Poly constitutive model. The Rolie–Poly constitutive equation is especially chosen because it expresses, precisely, the shear rheometry of polymer solutions for a large number of strain rates. For the Rolie–Poly approach, we use the two-fluid model wherein the stress dynamics are coupled with concentration equations. We follow a computational analysis approach via an efficient and versatile numerical algorithm. The numerical algorithm is based on the Finite Volume Method (FVM) and it is implemented in the open-source software package, OpenFOAM. The efficiency of our numerical algorithms is enhanced via two possible stabilization techniques, namely; the Log-Conformation Reformulation (LCR) and the Discrete Elastic Viscous Stress Splitting (DEVSS) methodologies. We demonstrate that our stabilized numerical algorithms accurately simulate these complex (shear banded) flows of complex (viscoelastic) fluids. Verification of the shear-banding results via both the Giesekus and Johnson-Segalman models show good agreement with existing literature using the DEVSS technique. A comparison of the Rolie–Poly two-fluid model results with existing literature for the concentration and velocity profiles is also in good agreement.