A stable numerical implementation of integral viscoelastic models in the OpenFOAM®computational library

This work presents the implementation and verification of a new solver in the OpenFOAM®open source computational library. The new solver allows the numerical solution of the integral viscoelastic constitutive equations, and their coupling with the continuity and momentum equations. This solver is also more stable when compared to the previous implementation of the group, which was accomplished through the addition of diffusive terms to both sides of the momentum equation, that are discretized using different schemes. The calculation of the Finger tensor follows the ideas presented in the method of deformation fields Peters et al. (2000) together with the modifications proposed by Tomé et al. (2008). We also propose a new approach to optimize the number and distribution of discretization points to be used in the time integration of the constitutive model, and the results obtained are discussed in the light of the recent work by Bollada and Phillips (2009). The solver is verified with three case studies: the steady Poiseuille and transient Couette flows, for a UCM fluid, and the steady 4:1 contraction flow, both for the UCM and K-BKZ fluids.