BEM-RBF approach for viscoelastic flow analysis

Tran-Cong, T. and Mai-Duy, N. and Phan-Thien, N. (2002) BEM-RBF approach for viscoelastic flow analysis. Engineering Analysis with Boundary Elements, 26 (9). pp. 757-762. ISSN 0955-7997


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 which 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 can be obtained by adding a particular solution (PS) 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 PS 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: Article (Commonwealth Reporting Category C)
Refereed: Yes
Item Status: Live Archive
Additional Information: © 2002 Elsevier Science Ltd. All rights reserved.
Faculty/School / Institute/Centre: Historic - Faculty of Engineering and Surveying - Department of Mechanical and Mechatronic Engineering (Up to 30 Jun 2013)
Faculty/School / Institute/Centre: Historic - Faculty of Engineering and Surveying - Department of Mechanical and Mechatronic Engineering (Up to 30 Jun 2013)
Date Deposited: 30 Nov 2007 11:47
Last Modified: 22 Oct 2013 01:44
Uncontrolled Keywords: BEM-PS-RBFN formulation; derivative approximation; function approximation; particular solution; viscoelastic flow
Fields of Research (2008): 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
Fields of Research (2020): 40 ENGINEERING > 4012 Fluid mechanics and thermal engineering > 401204 Computational methods in fluid flow, heat and mass transfer (incl. computational fluid dynamics)
49 MATHEMATICAL SCIENCES > 4901 Applied mathematics > 490101 Approximation theory and asymptotic methods
40 ENGINEERING > 4017 Mechanical engineering > 401706 Numerical modelling and mechanical characterisation
Socio-Economic Objectives (2008): E Expanding Knowledge > 97 Expanding Knowledge > 970109 Expanding Knowledge in Engineering
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