Direct numerical simulation of complex viscoelastic flows via fast lattice-Boltzmann solution of the Fokker–Planck equation

• Published in: Journal of non-Newtonian fluid mechanics Vol. 201; pp. 29 - 38
• Main Authors: Bergamasco, L., Izquierdo, S., Ammar, A.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.11.2013; Elsevier
• Subjects: Algorithms; Cylinders; Density; Differential equations; Engineering Sciences; FENE kinetic model; Finite volume method; Fluid mechanics; Fluids mechanics; Fokker-Planck equation; GPU computing; Lattice Boltzmann method; Mathematical models; Mechanics; Multi-scale; Physics; Sporting goods; Viscoelasticity; Finite volume method; Multi-scale; Lattice Boltzmann method; GPU computing; FENE kinetic model
• ISSN: 0377-0257; 1873-2631
• DOI: 10.1016/j.jnnfm.2013.07.004

•A novel micro–macro model for (FENE) viscoelastic flows is proposed.•The Fokker–Planck equation is solved by an operator-splitting procedure.•Finite volume method and lattice Boltzmann method are used for macro and micro-scales.•The model optimization is achieved by parametric analysis of the micro-scale equation.•The sub-grid solution is accelerated on graphic processing units by CUDA codes. Micro–macro simulations of polymeric solutions rely on the coupling between macroscopic conservation equations for the fluid flow and stochastic differential equations for kinetic viscoelastic models at the microscopic scale. In the present work we introduce a novel micro–macro numerical approach, where the macroscopic equations are solved by a finite-volume method and the microscopic equation by a lattice-Boltzmann one. The kinetic model is given by molecular analogy with a finitely extensible non-linear elastic (FENE) dumbbell and is deterministically solved through an equivalent Fokker–Planck equation. The key features of the proposed approach are: (i) a proper scaling and coupling between the micro lattice-Boltzmann solution and the macro finite-volume one; (ii) a fast microscopic solver thanks to an implementation for Graphic Processing Unit (GPU) and the local adaptivity of the lattice-Boltzmann mesh; (iii) an operator-splitting algorithm for the convection of the macroscopic viscoelastic stresses instead of the whole probability density of the dumbbell configuration. This latter feature allows the application of the proposed method to non-homogeneous flow conditions with low memory-storage requirements. The model optimization is achieved through an extensive analysis of the lattice-Boltzmann solution, which finally provides control on the numerical error and on the computational time. The resulting micro–macro model is validated against the benchmark problem of a viscoelastic flow past a confined cylinder and the results obtained confirm the validity of the approach.