Numerical simulation of two- and three-dimensional complex flows of viscoelastic fluids using the stream-tube method

The present paper examines the stream-tube method in two- and three-dimensional duct flows. The analysis uses the concept of stream-tubes in a mapped computational domain of the physical domain, where streamlines are parallel and straight. The primary unknown of the problem includes the transformation between the two domains, together with the pressure. Mass conservation is automatically verified by the formulation. Memory-integral constitutive equations may be considered without the particle-tracking problem. The method is applied to flows in contractions and a three-dimensional flow involving a threefold rotational symmetry. Viscous and elastic liquids involving memory-integral equations are investigated in the flow simulations. The discretized schemes for the unknowns are presented and the relevant equations solved by using optimization procedures such as the Levenberg-Marquardt and trust-region methods.