RBFN stochastic coarse-grained simulation method: Part I - Dilute polymer solutions using Bead-Spring Chain models
H.Q. Nguyen, C.-D. Tran and T. Tran-Cong

Source CMES: Computer Modeling in Engineering & Sciences, Vol. 105, No. 5, pp. 399-439, 2015
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Keywords Stochastic coarse-grained simulation, Brownian Configuration Fields, Integrated Radial basis function, nonlinear bead-spring chain models, hydrodynamic interaction, excluded volume.

In this paper, dynamic behaviours of dilute polymer solutions of various bead-spring chain models in shear flow are studied using a coarse-grained method based on the Integrated Radial Basis Function Networks (IRBFNs) and stochastic technique. The velocity field governed by the macroscopic conservation equations is determined by the IRBFN-based method, whereas the evolution of configurations of polymer chains governed by the diffusion stochastic differential equations are captured by the Brownian Configuration Field (BCF) approach. The system of micro-macro equations is closed by the Kramers’ expression, which allows for the determination of the polymer stresses in terms of BCF configurations. In this work, all nonlinear effects in a BSC model such as hydrodynamic interaction and excluded volume are considered. Since the simulation requires a considerable computational effort, parallel calculations are performed where possible. As an illustration of the method, the start-up planar Couette flow is examined, in which the evolution of viscometric functions such as shear stress, the first and the second normal stress differences is assessed with various BSC models.

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