Effective design approaches require the use of numerical modelling tools, to avoid long and high resource demanding experimental trial-and-error processes. The design tasks are even more difficult to undertake when dealing with complex rheology materials, as happens with the viscoelastic fluids, which present some counter intuitive phenomena. This framework has been motivating, during the last decades, the development of numerical modelling codes able to deal with viscoelastic fluids. The usual approaches employed, are based on segregated procedures, in which the mass, momentum and constitutive governing equations and solved iterative and sequentially. This sequential process is quite sensitive and prone to divergence, thus is often reported to require high relaxation factors, to assure the achievement of a converged solution. Moreover, the segregated approach is also know to limit substantially the Deborah numbers that can be achieved on the numerical calculation. This work reports the development of a coupled viscoelastic solver in OpenFOAM® computational library, in which the governing equations are solved simultaneously. The presented case studies clear evidence the advantages of the proposed approach, both in terms of calculation time and stability.