Computation of a Fokker-Planck-equation-based multi-scale model for complex flows using the IRBFN method

Tran, Canh-Dung and Mai-Duy, Nam and Tran-Cong, Thanh (2012) Computation of a Fokker-Planck-equation-based multi-scale model for complex flows using the IRBFN method. In: 6th European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2012), 10-14 Sep 2012, Vienna, Austria.


This paper presents a numerical approach based on the Integrated Radial Basis Functions (IRBF) for the Fokker Planck Equation (FPE) macro-micro multi-scale models of visco-elastic fluid flows. The FPE is for the calculation of extra stress and the conservation equations for the velocity field. In this approach, the stress is decoupled
from the velocity field and computed deterministically without the need for a closed form rheological constitutive equation. The FPEs and momentum conservation equations are
discretised using a spatially local collocation method where the IRBF based approximants improve the accuracy of the numerical solutions by avoiding the deterioration of
accuracy caused by differentiation. The method is illustrated with the time evolution of the planar Couette flow of a Hookean dumbbell model fluid.

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Item Type: Conference or Workshop Item (Commonwealth Reporting Category E) (Paper)
Refereed: Yes
Item Status: Live Archive
Faculty / Department / School: Historic - Faculty of Engineering and Surveying - Department of Mechanical and Mechatronic Engineering
Date Deposited: 15 Apr 2013 02:04
Last Modified: 18 Sep 2014 03:43
Uncontrolled Keywords: multiscale computation; fokker-planck equation; Brownian configuration field method; complex fluid flows; integrated radial basis function networks; macro-micro multi-scale method; stochastic simulation
Fields of Research : 01 Mathematical Sciences > 0103 Numerical and Computational Mathematics > 010302 Numerical Solution of Differential and Integral Equations
09 Engineering > 0915 Interdisciplinary Engineering > 091501 Computational Fluid Dynamics
09 Engineering > 0913 Mechanical Engineering > 091307 Numerical Modelling and Mechanical Characterisation
Socio-Economic Objective: E Expanding Knowledge > 97 Expanding Knowledge > 970109 Expanding Knowledge in Engineering
E Expanding Knowledge > 97 Expanding Knowledge > 970101 Expanding Knowledge in the Mathematical Sciences

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