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
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 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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