A Multiscale Method Based on the Fibre Configuration Field, IRBF and DAVSS for the Simulation of Fibre Suspension Flows
H.Q. Nguyen, C.-D. Tran and T. Tran-Cong

doi:10.3970/cmes.2015.109.361
Source CMES: Computer Modeling in Engineering & Sciences, Vol. 109, No. 4, pp. 361-403, 2015
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Keywords Fibre Configuration Field, Integrated Radial Basis Function, Dilute fibre suspension flow, Jeffery equation, Lipscomb model, Discrete adaptive viscoelastic stress splitting, Multiscale simulation method.
Abstract

In this paper, an Integrated Radial Basis Function (IRBF)-based multiscale method is used to simulate the rheological properties of dilute fibre suspensions. For the approach, a fusion of the IRBF computation scheme, the Discrete Adaptive Viscoelastic Stress Splitting (DAVSS) technique and the Fibre Configuration Field has been developed to investigate the evolution of the flow and the fibre configurations through two separate computational processes. Indeed, the flow conservation equations, which are expressed in vorticity-stream function formulation, are solved using IRBF-based numerical schemes while the evolution of fibre configuration fields governed by the Jeffery’s equation is captured using the principle of Brownian Configuration Fields. The two procedures are coupled together by the Lipscomb expression which is used to determine the fibre stress of dilute fibre suspensions. Owing to advantages of the IRBF scheme and the DAVSS technique, the present method yields a more accurate solution and faster convergence rate. The simulation method is verified and its capability is demonstrated with the fibre suspension flows through two parallel plates, a circular tube and the 4:1 and 4.5:1 axisymmetric contraction geometries which are usually chosen to test a numerical method because of the challenging nature of these problems.

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