BEM-RBF approach for viscoelastic flow analysis

Tran-Cong, T. and Mai-Duy, N. and Phan-Thien, N. (2001) BEM-RBF approach for viscoelastic flow analysis. In: 23rd International Conference on the Boundary Element Method (BEM 2001), 7-9 May 2001, Lemnos, Greece.

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Abstract

A new BE-only method is achieved for the numerical solution of viscoelastic flows. A decoupled algorithm is chosen where the fluid is considered as being composed of an artificial Newtonian component and the remaining component is accordingly defined from the original constitutive equation. As a result the problem is viewed as that of solving for the flow of a Newtonian liquid with the non-linear viscoelastic effects acting as a pseudo body force. Thus the general solution is obtained by adding a particular solution to the homogeneous one. The former is obtained by a BEM for the base Newtonian fluid and the latter is obtained analytically by approximating the pseudo body force in terms of suitable radial basis functions (RBFs). Embedded in the approximation of the pseudo body force is the calculation of the polymer stress. This is achieved by solving the constitutive equation using RBF networks (RBFNs). Both the calculations of the particular solution and the polymer stress are therefore meshless and the resultant BEM-RBF method is a BE-only method. The complete elimination of any structured domain discretisation is demonstrated with a number of flow problems involving the Upper Convected Maxwell (UCM) and the Oldroyd-B fluids.


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Item Type: Conference or Workshop Item (Commonwealth Reporting Category E) (Paper)
Refereed: Yes
Item Status: Live Archive
Additional Information: Series title: Advances in Boundary Elements v.10
Faculty / Department / School: Historic - Faculty of Engineering and Surveying - No Department
Date Deposited: 30 Nov 2007 11:55
Last Modified: 22 Oct 2013 02:20
Uncontrolled Keywords: BEM-PS-RBFN formulation; derivative approximation; function approximation; particular solution; viscoelastic flow
Fields of Research : 09 Engineering > 0915 Interdisciplinary Engineering > 091501 Computational Fluid Dynamics
01 Mathematical Sciences > 0102 Applied Mathematics > 010201 Approximation Theory and Asymptotic Methods
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
Identification Number or DOI: 10.2495/BE010301
URI: http://eprints.usq.edu.au/id/eprint/10983

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