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

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  • Normandin, Magdeleine
  • Clermont, Jean-Robert
  • Mahmoud, Ahmad

Abstract

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.

Suggested Citation

  • Normandin, Magdeleine & Clermont, Jean-Robert & Mahmoud, Ahmad, 2000. "Laminar flow calculations in ducts of complex shapes using mapping functions and decomposition of domains," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 52(1), pages 21-39.
    • Handle: RePEc:eee:matcom:v:52:y:2000:i:1:p:21-39
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    References listed on IDEAS

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    1. Béreaux, Yves & Clermont, Jean-Robert, 1997. "Numerical simulation of two- and three-dimensional complex flows of viscoelastic fluids using the stream-tube method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 44(4), pages 387-400.
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    1. Normandin, Magdeleine & Radu, Dana Grecov & Mahmoud, Ahmad & Clermont, Jean-Robert, 2002. "Finite element and stream-tube formulations for flow computations—two-dimensional applications," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 60(1), pages 129-134.

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