Abstract
We introduce a numerical method for solving the coupled Navier-Stokes-Fokker-Planck model (i.e. a micro-macro model) for dilute polymeric fluids where polymer molecules are modelled as FENE dumbbells. The Fokker-Planck equation is posed on a high-dimensional domain and is therefore challenging from a computational point of view. We summarise analytical results for a Galerkin spectral method for the Fokker-Planck equation in configuration space, before combining this method with a finite element scheme in physical space to obtain an alternating-direction method for the high-dimensional Fokker-Planck equation. Alternating-direction methods have been considered previously in he literature for this problem (e.g. by Chauvière & Lozinski); we present an alternative frame-work here that is underpinned by rigorous numerical analysis, and numerical results demonstrating the effectiveness of our approach. The algorithm is well suited to implementation on a parallel computer, and we exploit this fact to make large-scale computations feasible.
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Knezevic, D.J., Süli, E. (2009). A Deterministic Multiscale Approach for Simulating Dilute Polymeric Fluids. In: Hegarty, A., Kopteva, N., O'Riordan, E., Stynes, M. (eds) BAIL 2008 - Boundary and Interior Layers. Lecture Notes in Computational Science and Engineering, vol 69. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00605-0_2
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