Abstract
We present a numerical scheme for a previously unexploited formulation of the equations for unsteady viscoelastic flow. The formulation aligns the polymer stress along particle paths/streamlines, utilising the characteristic curves associated with the hyperbolic part of the constitutive equations. We illustrate the approach for the Oldroyd-B model in the benchmark 4:1 contraction for moderate elasticity numbers. We show that the scheme is able to accurately capture the re-entrant corner singularity for the polymer stresses and the pressure, the latter variable being inaccurately determined by schemes using the traditional formulation in terms of Cartesian polymer stresses. A space-step restriction for stability is derived, which can be numerically limiting in certain recirculation regions. This contrasts with the equivalent space-step restriction for the formulation in Cartesian stresses, which is limiting in flow regions of high velocity gradients, for example, at sharp corners in contraction flows.
| Language | English |
|---|---|
| Pages | 462-489 |
| Number of pages | 28 |
| Journal | Journal of Computational Physics |
| Volume | 388 |
| Early online date | 23 Mar 2019 |
| DOIs | |
| Status | Published - 1 Jul 2019 |
Keywords
- Natural Stress Formulation
- Numerical simulation
- Sharp corner flows
- Unsteady viscoelastic flows
ASJC Scopus subject areas
- Physics and Astronomy (miscellaneous)
- Computer Science Applications
Cite this
Application of the natural stress formulation for solving unsteady viscoelastic contraction flows. / Evans, Jonathan D.; França, Hugo L.; Oishi, Cassio M.
In: Journal of Computational Physics, Vol. 388, 01.07.2019, p. 462-489.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Application of the natural stress formulation for solving unsteady viscoelastic contraction flows
AU - Evans, Jonathan D.
AU - França, Hugo L.
AU - Oishi, Cassio M.
PY - 2019/7/1
Y1 - 2019/7/1
N2 - We present a numerical scheme for a previously unexploited formulation of the equations for unsteady viscoelastic flow. The formulation aligns the polymer stress along particle paths/streamlines, utilising the characteristic curves associated with the hyperbolic part of the constitutive equations. We illustrate the approach for the Oldroyd-B model in the benchmark 4:1 contraction for moderate elasticity numbers. We show that the scheme is able to accurately capture the re-entrant corner singularity for the polymer stresses and the pressure, the latter variable being inaccurately determined by schemes using the traditional formulation in terms of Cartesian polymer stresses. A space-step restriction for stability is derived, which can be numerically limiting in certain recirculation regions. This contrasts with the equivalent space-step restriction for the formulation in Cartesian stresses, which is limiting in flow regions of high velocity gradients, for example, at sharp corners in contraction flows.
AB - We present a numerical scheme for a previously unexploited formulation of the equations for unsteady viscoelastic flow. The formulation aligns the polymer stress along particle paths/streamlines, utilising the characteristic curves associated with the hyperbolic part of the constitutive equations. We illustrate the approach for the Oldroyd-B model in the benchmark 4:1 contraction for moderate elasticity numbers. We show that the scheme is able to accurately capture the re-entrant corner singularity for the polymer stresses and the pressure, the latter variable being inaccurately determined by schemes using the traditional formulation in terms of Cartesian polymer stresses. A space-step restriction for stability is derived, which can be numerically limiting in certain recirculation regions. This contrasts with the equivalent space-step restriction for the formulation in Cartesian stresses, which is limiting in flow regions of high velocity gradients, for example, at sharp corners in contraction flows.
KW - Natural Stress Formulation
KW - Numerical simulation
KW - Sharp corner flows
KW - Unsteady viscoelastic flows
UR - http://www.scopus.com/inward/record.url?scp=85063646304&partnerID=8YFLogxK
U2 - 10.1016/j.jcp.2019.02.045
DO - 10.1016/j.jcp.2019.02.045
M3 - Article
VL - 388
SP - 462
EP - 489
JO - Journal of Computational Physics
T2 - Journal of Computational Physics
JF - Journal of Computational Physics
SN - 0021-9991
ER -