NUMERICAL-SIMULATION OF 2-DIMENSIONAL AND 3-DIMENSIONAL COMPLEX FLOWSOF VISCOELASTIC FLUIDS USING THE STREAM-TUBE METHOD

The present paper examines the stream-tube method in two-and three-dim ensional duct flows. The analysis uses the concept of stream-tubes in a mapped computational domain of the physical domain, where streamline s are parallel and straight, The primary unknown of the problem includ es the transformation between the two domains, together with the press ure. Mass conservation is automatically verified by the formulation. M emory-integral constitutive equations may be considered without the pa rticle-tracking problem. The method is applied to flows in contraction s and a three-dimensional flow involving a threefold rotational symmet ry. Viscous and elastic liquids involving memory-integral equations ar e investigated in the flow simulations. The discretized schemes for th e unknowns are presented and the relevant equations solved by using op timization procedures such as the Levenberg-Marquardt and trust-region methods.