Journal ArticleDOI
A simple method for simulating general viscoelastic fluid flows with an alternate log-conformation formulation
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TLDR
Hulsen et al. as mentioned in this paper used the log-conformation formulation to solve the high Weissenberg number problem for viscoelastic flow problems, which can be used to solve all the governing equations (continuity, conservation of momentum and constitutive equation) in a strongly coupled way.Abstract:
The log-conformation formulation has alleviated the long-standing high Weissenberg number problem associated with the viscoelastic fluid flows [R. Fattal, R. Kupferman, Constitutive laws for the matrix-logarithm of the conformation tensor, J. Non-Newtonian Fluid Mech. 123 (2004) 281–285]. This formulation ensures that solutions of viscoelastic flow problems are physically admissible, and it is able to capture sharp elastic stress layers. However, the implementations presented in literature thus far require changing the evolution equation for the conformation tensor into an equation for its logarithm, and are based on loosely coupled (partitioned) solution procedures [M.A. Hulsen, et al., Flow of viscoelastic fluids past a cylinder at high Weissenberg number: stabilized simulations using matrix logarithms, J. Non-Newtonian Fluid Mech. 127 (2005) 27–39]. A simple alternate form of the log-conformation formulation is presented in this article, and an implementation is demonstrated in the DEVSS-TG/SUPG finite element method. Besides its straightforward implementation, the new log-conformation formulation can be used to solve all the governing equations (continuity, conservation of momentum and constitutive equation) in a strongly coupled way by Newton’s method. The method can be applied to any conformation tensor model. The flows of Oldroyd-B and Larson-type fluids are tested in the benchmark problem of a flow past a cylinder in a channel. The accuracy of the method is assessed by comparing solutions with published results. The benefits of this new implementation and the pending issues are discussed.read more
Citations
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Journal ArticleDOI
The log-conformation tensor approach in the finite-volume method framework
Alexandre M. Afonso,Paulo J. Oliveira,Fernando T. Pinho,Fernando T. Pinho,Maria Arminda Costa Alves +4 more
TL;DR: In this paper, the performance of the log-conformation formulation in the Finite Volume Method (FVM) framework for creeping flows of viscoelastic fluids in steady and unsteady flows around a confined cylinder was investigated.
Journal ArticleDOI
Numerical Methods for Viscoelastic Fluid Flows
TL;DR: In this paper, the addition of macromolecules to a solvent imparts viscoelasticity to the solvability of complex fluids, which can be used for specific applications.
Journal ArticleDOI
Dynamics of high-Deborah-number entry flows: a numerical study
TL;DR: In this paper, high-elasticity simulations of flows through a 2D 4 : 1 abrupt contraction and a 3D square-square abrupt contraction were performed with a finite-volume method implementing the log-conformation formulation, proposed by Fattal & Kupferman (J. Non-Newtonian Fluid Mech., vol. 123, 2004, p. 281) to alleviate the high Weissenberg-number problem.
Journal ArticleDOI
A monolithic FEM approach for the log-conformation reformulation (LCR) of viscoelastic flow problems
TL;DR: The presented methodology, for the well-known ‘flow around cylinder’ benchmark problem, is that it is possible to do a direct steady approach and to avoid pseudo-time stepping with correspondingly small time step sizes in the case of a nonsteady approach.
Journal ArticleDOI
On the simulation of a time‐dependent cavity flow of an Oldroyd‐B fluid
TL;DR: In this paper, a finite element method for simulating the time-dependent flow of an Oldroyd-B fluid in a lid-driven cavity is presented, where the key considerations for developing the methodology are the preservation of the positive definiteness of the conformation tensor via the log-conformation representation and additional diffusion, from second-order upwind scheme, to smooth the highfrequency modes.
References
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