Laminar flow calculations in ducts of complex shapes using mapping functions and decomposition of domains

The method presented in this paper, based on geometrical considerations, co ncerns the use of unknown transformations and decomposition of domains for computation of fully-developed flows in ducts of complex shape. The approac h involves local one-to-one transformations of sub-domains of the physical two-dimensional domain into simple mapped domains used for computation, whe re a rectangular mesh can be defined. The formulation allows direct calcula tion of velocity contour values in flow regions close to the boundaries, av oiding problems that may arise from geometrical singularities in shape of t he physical domain. Application of the method are given for different types of ducts with fluids obeying various constitutive equations. The set of go verning equations is solved by the means of the Levenberg-Marquardt optimiz ation algorithm. (C) 2000 Published by Elsevier Science B.V. All rights res erved.