Multiscale stochastic simulation of transient complex flows

Multiscale stochastic simulation of transient complex flows

The thesis reports new multiscale simulation methods to predict rheological properties of complex fluids. Dilute polymer solutions, polymer melts and fibre suspensions with a Newtonian matrix are the main interests of this study. In the present multiscale approach, the stress contributed by polymers or suspended fibres is determined by the Brownian configuration field (BCF) method using kinetic models whereas integrated radial basis function (IRBF) based numerical methods are used to approximate field variables and their derivatives and to discretise governing equations. The macro-micro multiscale system is linked together by a stress formula by kinetic models.

The IRBF-BCF based multiscale method is first applied to simulate dilute polymer solutions modelled by bead-spring chains (BSCs), incorporating finitely extensible nonlinear elastic springs, hydrodynamic interaction and excluded volume effects. Then, the simulation method is further developed for polymer melt systems, in which the entanglement of polymer molecules is described by Doi-Edwards, Curtiss-Bird, reptating rope and double reptation models. The numerical stability of the method, which is generally known as a challenging problem in the simulation of polymer melts, is enhanced owing to the combination of the IRBF method and the BCF idea. As an illustration of the method, the start-up Couette flow and the flow over a cylinder in a channel are investigated for both dilute polymer solutions and polymer melts.

A new multiscale approach is also developed to simulate the rheological characteristics of fibre suspensions in both dilute and non-dilute regimes. The approach is a combination of the IRBF scheme, the discrete adaptive viscoelastic stress splitting (DAVSS) formulation and the BCF idea. The macroscopic conservation equations described in stream function-vorticity formulation are solved using the 1D-IRBF scheme combined with the DAVSS technique. The evolution equation for fibre configuration fields governed by the Jeffery equation for dilute fibre suspensions or the Folgar-Tucker equation for non-dilute fibre suspensions is explicitly advanced in time using the BCF approach. The fibre stress is determined based one fibre configuration fields using the Lipscomb and Phan-Thien–Graham models for dilute and non-dilute fibre suspensions, respectively. The method is verified with the simulation of flows of fibre suspensions between two parallel plates, flows through a circular tube, the 4:1 and 4.5:1 axisymmetric contraction flows, and the 1:4 axisymmetric expansion flows.

Numerical experiments confirm the present method efficiency based on both the enhanced convergence rate of the solution and the stability of a stochastic process.