A semi-Lagrangian micro–macro method for viscoelastic flow calculations

We present in this paper a semi-Lagrangian algorithm to calculate the viscoelastic flow in which a dilute polymer solution is modeled by the FENE dumbbell kinetic model. In this algorithm the material derivative operator of the Navier–Stokes equations (the macroscopic flow equations) is discretized...

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Bibliographic Details
Published in:Journal of non-Newtonian fluid mechanics Vol. 165; no. 3; pp. 120 - 135
Main Authors: Prieto, Juan Luis, Bermejo, Rodolfo, Laso, Manuel
Format: Journal Article
Language:English
Published: Oxford Elsevier B.V 01.02.2010
Elsevier
Subjects:
Applied sciences
Characteristics
Exact sciences and technology
Finite element
Micro–macro
Organic polymers
Physicochemistry of polymers
Properties and characterization
Semi-Lagrangian scheme
Solution and gel properties
Micro–macro
Characteristics
Semi-Lagrangian scheme
Finite element
Viscoelasticity
Chemical solution
Pipe flow
Theoretical study
Polymer
Modeling
Finite element method
Sudden contraction
Micro-macro
Dumbbell model
Dilute solution
Numerical simulation
Lagrangian method
Rheological properties
ISSN:0377-0257, 1873-2631
Online Access:Get full text
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Summary:We present in this paper a semi-Lagrangian algorithm to calculate the viscoelastic flow in which a dilute polymer solution is modeled by the FENE dumbbell kinetic model. In this algorithm the material derivative operator of the Navier–Stokes equations (the macroscopic flow equations) is discretized in time by a semi-Lagrangian formulation of the second order backward difference formula (BDF2). This discretization leads to solving each time step a linear generalized Stokes problem. For the stochastic differential equations of the microscopic scale model, we use the second order predictor-corrector scheme proposed in [22] applied along the forward trajectories of the center of mass of the dumbbells. Important features of the algorithm are (1) the new semi-Lagrangian projection scheme; (2) the scheme to move and locate both the mesh-points and the dumbbells; and (3) the calculation and space discretization of the polymer stress. The algorithm has been tested on the 2d 10:1 contraction benchmark problem and has proved to be accurate and stable, being able to deal with flows at high Weissenberg ( W i ) numbers; specifically, by adjusting the size of the time step we obtain solutions at W i = 444 .
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ISSN:0377-0257
1873-2631
DOI:10.1016/j.jnnfm.2009.10.004