Abstract
An Integrated RBFN-Based Macro-Micro Multi-Scale Method for Computation of Visco-Elastic Fluid Flows
Highlights
A common approach for the computation and analysis of complex fluid flows has been based on the coupling of the system of mass and momentum conservation equations with appropriate closed form constitutive equations
The convergence measures (CM) for the shear stress and the first normal stress difference are around 10−3 10−4 and show that results obtained by the present method are in good agreement with the analytical solution given by Eq (54)
The results showed that the present method is able to produce a high degree accuracy using a relatively coarse grid, insufficient number of dumbbells at each collocation point will result in oscillatory behaviours even with variance reduction method
Summary
A common approach for the computation and analysis of complex fluid flows has been based on the coupling of the system of mass and momentum conservation equations with appropriate closed form constitutive equations. A number of advanced numerical methods have been developed to appropriately deal with the above issues Among these methods, the multiscale methods [Engquist, Lötstedt, and Runborg (2000); Allaire and Brizzi (2005); Chu, Efendiev, Ginting, and Hou (2008); Hou (2005); Hajibeygi, Gonfigli, Hesse, and Jenny (2008)] have attracted significant attention for the last two decades. The main idea of these techniques is that the polymer contribution to the stress is directly calculated from a large ensemble of microscopic configurations without having to derive a closed form constitutive equation, which is a powerful feature for the modelling of materials [Ottinger (1996); Engquist, Lötstedt, and Runborg (2000)].
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