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, concerns the use of unknown transformations and decomposition of domains for computation of fully-developed flows in ducts of complex shape. The approach involves local one-to-one transformations of sub-domains of the physical two-dimensional domain into simple mapped domains used for computation, where a rectangular mesh can be defined. The formulation allows direct calculation of velocity contour values in flow regions close to the boundaries, avoiding problems that may arise from geometrical singularities in shape of the physical domain. Application of the method are given for different types of ducts with fluids obeying various constitutive equations. The set of governing equations is solved by the means of the Levenberg–Marquardt optimization algorithm.