Deterministic and stochastic algorithms for resolving the flow fields in ducts and networks using energy minimization

Taha Sochi ()
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Taha Sochi: Department of Physics & Astronomy, University College London, Gower Street, WC1E 6BT, London

International Journal of Modern Physics C (IJMPC), 2016, vol. 27, issue 04, 1-12

Abstract: Several deterministic and stochastic multi-variable global optimization algorithms (Conjugate Gradient, Nelder–Mead, Quasi-Newton and global) are investigated in conjunction with energy minimization principle to resolve the pressure and volumetric flow rate fields in single ducts and networks of interconnected ducts. The algorithms are tested with seven types of fluid: Newtonian, power law, Bingham, Herschel–Bulkley, Ellis, Ree–Eyring and Casson. The results obtained from all those algorithms for all these types of fluid agree very well with the analytically derived solutions as obtained from the traditional methods which are based on the conservation principles and fluid constitutive relations. The results confirm and generalize the findings of our previous investigations that the energy minimization principle is at the heart of the flow dynamics systems. The investigation also enriches the methods of computational fluid dynamics for solving the flow fields in tubes and networks for various types of Newtonian and non-Newtonian fluids.

Keywords: Energy minimization; fluid dynamics; global multi-variable optimization; pressure; flow rate; tube; network; deterministic; stochastic; Conjugate Gradient; Nelder–Mead; Quasi-Newton; global; Newtonian; power law; Bingham; Herschel–Bulkley; Ellis; Ree–Eyring; Casson (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1142/S0129183116500364

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