Abstract
The multiscale stochastic simulation method based on the marriage of the Brownian Configuration Field (BCF) and the Radial Basis Function mesh-free approximation for dilute fibre suspensions by our group, is further developed to simulate non-dilute fibre suspensions. For the present approach, the macro and micro processes proceeded at each time step are linked to each other by a fibre contributed stress formula associated with the used kinetic model. Due to the feature of non-dilute fibre suspensions, the interaction between fibres is introduced into the evolution equation to determine fibre configurations using the BCF method. The fibre stresses are then determined based on the fibre configuration fields using the Phan–Thien–Graham model. The efficiency of the simulation method is demonstrated by the analysis of the two challenging problems, the axisymmetric contraction and expansion flows, for a range of the fibre concentration from semi-dilute to concentrated regimes. Results evidenced by numerical experiments show that the present method would be potential in analysing and simulating various suspensions in food and medical industries.
Highlights
The regime of a suspension flow is based on two parameters: the aspect ratio ar and the volume fraction
Results show a significant influence of a2r on the convergence of the method, where the convergence measure (CM) generally degenerates with increasing level of fibre concentration and/or aspect ratio
The multiscale simulation method based on the combination of high-order integral RBF approximation and Brownian Configuration Field (BCF) idea is further developed for non-dilute fibre suspensions in this work
Summary
The regime of a suspension flow is based on two parameters: the aspect ratio ar and the volume fraction. Owing to the advantages of RBF-based high-order approximation schemes, the approach achieved high-order convergence and accuracy Nguyen et al [16, 17] Aligning with this approach, high-order RBF-based Brownian configuration field (BCF) method for dilute fibre suspensions Nguyen et al [17] by our group is further developed for non-dilute suspensions by introducing a diffusion term into the Jeffery equation to capture fibre–fibre interaction. High-order RBF-based Brownian configuration field (BCF) method for dilute fibre suspensions Nguyen et al [17] by our group is further developed for non-dilute suspensions by introducing a diffusion term into the Jeffery equation to capture fibre–fibre interaction For this scheme, the conservation equations using the vorticity-stream function form are discretised using the high-order integrated RBF scheme, whereas the fibre configurations governed by the Folgar–Tucker equation are advanced by the BCF approach.
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