A numerical solution based on the Fokker-Planck equation for dilute polymer solutions using high order RBF methods

Nguyen, H. Q. and Tran, C.-D. and Pham-Sy, N. and Tran-Cong, T. (2014) A numerical solution based on the Fokker-Planck equation for dilute polymer solutions using high order RBF methods. Applied Mechanics and Materials, 553. pp. 187-192. ISSN 1662-7482


This paper presents a numerical method for the Fokker-Planck Equation (FPE) based on mesoscopic modelling of dilute polymer solutions using Radial Basis Function (RBF) approaches. The stress is determined by the solution of a FPE while the velocity field is locally calculated via the
solution of conservation Differential Equations (DEs) [1,2]. The FPE and PDEs are approximated separately by two different Integrated RBF methods. The time implicit discretisation of both FPE and PDEs is carried out using collocation methods where the high order RBF approximants improve significantly the accuracy of the numerical solutions and the convergence rate. As an illustration of the method, the time evolution of a start-up flow is studied for the Finitely Extensible Nonlinear Elastic (FENE) dumbbell model.

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Item Type: Article (Commonwealth Reporting Category C)
Refereed: Yes
Item Status: Live Archive
Additional Information: © (2014) Trans Tech Publications, Switzerland. Permanent restricted access to published version in accordance with the copyright policy of the publisher. Paper presented at: 1st Australasian Conference on Computational Mechanics (ACCM 2013) held in Sydney 3-4 Oct 2013.
Faculty/School / Institute/Centre: Current - Faculty of Health, Engineering and Sciences - School of Mechanical and Electrical Engineering
Date Deposited: 09 Jul 2014 00:21
Last Modified: 04 Jul 2016 05:03
Uncontrolled Keywords: Fokker-Planck equation; dilute polymer solution; high order RBF methods; parallel technique
Fields of Research : 01 Mathematical Sciences > 0104 Statistics > 010406 Stochastic Analysis and Modelling
09 Engineering > 0915 Interdisciplinary Engineering > 091501 Computational Fluid Dynamics
09 Engineering > 0912 Materials Engineering > 091209 Polymers and Plastics
Socio-Economic Objective: E Expanding Knowledge > 97 Expanding Knowledge > 970109 Expanding Knowledge in Engineering
Identification Number or DOI: 10.4028/www.scientific.net/AMM.553.187
URI: http://eprints.usq.edu.au/id/eprint/25262

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