Numerical simulation of three-dimensional duct flows of incompressible fluids by using the stream-tube method

Numerical simulation of three-dimensional flows generally involves solving large-scale problems. In this paper we consider the stream-tube method in three-dimensional duct flows. The analysis uses the concept of stream tubes in a mapped computational domain of the physical domain where the streamlines are parallel and straight. The incompressibility equation is automatically verified and the primary unknowns of the problem are, in addition to the pressure, the transformation functions between the two domains. It is also shown that the flow may be computed by considering successive subdomains (the stream tubes). This results in a reduction of computing time and storage area. Incompressible viscous and elastic liquids involving memory-integral equations may be considered in the flow simulations. This part of the paper examines three-dimensional flows of Newtonian fluids. The method is applied to the flow in a duct involving a threefold rotational symmetry, where the discretized relevant equations are solved by using the Levenberg-Marquardt algorithm.