A fast and efficient iterative scheme for viscoelastic flow simulations with the DEVSS finite element method

We present a new fast iterative solution technique for the large sparse-matrix system that is commonly encountered in the mixed finite-element formulation of transient viscoelastic flow simulation: the DEVSS (discrete elastic-viscous stress splitting) method. A block-structured preconditioner for th...

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Bibliographic Details
Published in:Journal of non-Newtonian fluid mechanics 2011-04, Vol.166 (7), p.354-362
Main Authors: Hwang, Wook Ryol, Walkley, Mark A., Harlen, Oliver G.
Format: Article
Language:English
Subjects:
Algebraic multigrid method
Block preconditioning
Blocking
Computational methods in fluid dynamics
Discrete elastic-viscous stress splitting (DEVSS)
Discrete systems
Exact sciences and technology
Finite element method
Flow simulation
Fluid dynamics
Fundamental areas of phenomenology (including applications)
Iterative methods
Iterative solver
Mathematical analysis
Non-newtonian fluid flows
Physics
Preconditioning
Solvers
Viscoelastic flow simulation
Viscoelasticity
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Summary:We present a new fast iterative solution technique for the large sparse-matrix system that is commonly encountered in the mixed finite-element formulation of transient viscoelastic flow simulation: the DEVSS (discrete elastic-viscous stress splitting) method. A block-structured preconditioner for the velocity, pressure and viscous polymer stress has been proposed, based on a block reduction of the discrete system, designed to maintain spectral equivalence with the discrete system. The algebraic multigrid method and the diagonally scaled conjugate gradient method are applied to the preconditioning sub-block systems and a Krylov subspace iterative method (MINRES) is employed as an outer solver. We report the performance of the present solver through example problems in 2D and 3D, in comparison with the corresponding Stokes problems, and demonstrate that the outer iteration, as well as each block preconditioning sub-problem, can be solved within a fixed number of iterations. The required CPU time for the entire problem scales linearly with the number of degrees of freedom, indicating O(N) performance of this solution algorithm.
ISSN:0377-0257
1873-2631
DOI:10.1016/j.jnnfm.2011.01.003