BEM-NN computation of generalised Newtonian flows

Tran, Canh-D. and Tran-Cong, T. (2002) BEM-NN computation of generalised Newtonian flows. Engineering Analysis with Boundary Elements, 26 (1). pp. 15-28. ISSN 0955-7997


This paper presents a boundary-element-only method (BEM) for the calculation of generalised Newtonian fluid (GNF)fows. The volume integral arising from nonlinear effects is approximated via a particular solution technique. Multilayer
Perceptron networks (MLPN) and Radial Basis Function Networks (RBFN) are used for global approximation of field variables and hence volume discretisation is not required. The iterative numerical formulation is achieved by viewing the material as being composed of a Newtonian base (artificially assigned with a constant, but maybe different from subdomain to subdomain, viscosity) and the remaining component which is accordingly defined from the original constitutive equation. This decoupling of the nonlinear effects allows a Picard-type iterative procedure to
be employed by treating the nonlinear term as a known forcing function. However, convergence is sensitive to the estimate of this forcing function and an adaptive subregioning of the domain is adopted to control the accuracy of the estimate of this nonlinear term. The criterion for subregioning is that the velocity gradient should not vary significantly in each subdomain. This strategy enables convergence of the present method (BEM-NN) at power-law index as low as 0:2 for the difficult power
law fluid. The use of MLPNs (instead of single layer peceptrons) and RBFNs is another contributing factor to the improved convergence performance. The overall scheme is very suitable for coarse-grain parallelisation as each subdomain can be independently analysed within an iteration.Furthermore, within each subdomain process there are other parallelisable computations. The present method is verified with circular Couette and planar Poiseuille
ows of the power-law, Carreau-Yasuda and Cross fluids.

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Item Type: Article (Commonwealth Reporting Category C)
Refereed: Yes
Item Status: Live Archive
Additional Information: Accepted version deposited in accordance with the copyright policy of the publisher
Faculty / Department / School: Historic - Faculty of Engineering and Surveying - Department of Mechanical and Mechatronic Engineering
Date Deposited: 03 Aug 2011 01:35
Last Modified: 13 Sep 2013 02:32
Uncontrolled Keywords: BEM; FFNN; GNF; MLPN; RBFN; boundary element; generalised Newtonian flow; neural network
Fields of Research : 01 Mathematical Sciences > 0103 Numerical and Computational Mathematics > 010302 Numerical Solution of Differential and Integral Equations
09 Engineering > 0915 Interdisciplinary Engineering > 091504 Fluidisation and Fluid Mechanics
09 Engineering > 0913 Mechanical Engineering > 091307 Numerical Modelling and Mechanical Characterisation
Socio-Economic Objective: E Expanding Knowledge > 97 Expanding Knowledge > 970109 Expanding Knowledge in Engineering
E Expanding Knowledge > 97 Expanding Knowledge > 970101 Expanding Knowledge in the Mathematical Sciences
Identification Number or DOI: doi: 10.1016/S0955-7997(01)00085-6

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