A numerical approach for computing flows by local transformations and domain decomposition using an optimization algorithm Original Research Article

This paper presents theoretical information for numerical simulation of two- and three-dimensional flows, based on the concepts of streamlines and local transformation functions associated with domain decomposition. In this approach, in addition to the pressure, the primary unknowns are the local mapping functions between the physical sub-domains and transformed domains where the mapped streamlines are parallel straight lines. This makes it easy to handle time-dependent constitutive equations for complex fluids. To solve the governing equations that also involve compatibility equations between sub-domains, an optimization algorithm is set up in order to compute the unknowns related to the streamlines iteratively. Applications are given for two-dimensional flows between eccentric cylinders, using different constitutive equations.