### Abstract

Numerical simulations reveal the formation of singular structures in the polymer stress field of a viscoelastic fluid modeled by the Oldroyd-B equations driven by a simple body force. These singularities emerge exponentially in time at hyperbolic stagnation points in the flow and their algebraic structure depends critically on the Weissenberg number. Beyond a first critical Weissenberg number the stress field approaches a cusp singularity, and beyond a second critical Weissenberg number the stress becomes unbounded exponentially in time. A local approximation to the solution at the hyperbolic point is derived from a simple ansatz, and there is excellent agreement between the local solution and the simulations. Although the stress field becomes unbounded for a sufficiently large Weissenberg number, the resultant forces of stress grow subexponentially. Enforcing finite polymer chain lengths via a FENE-P penalization appears to keep the stress bounded, but a cusp singularity is still approached exponentially in time.

Original language | English (US) |
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Article number | 103103 |

Journal | Physics of Fluids |

Volume | 19 |

Issue number | 10 |

DOIs | |

State | Published - Oct 2007 |

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### ASJC Scopus subject areas

- Fluid Flow and Transfer Processes
- Computational Mechanics
- Mechanics of Materials
- Physics and Astronomy(all)
- Condensed Matter Physics

### Cite this

*Physics of Fluids*,

*19*(10), [103103]. https://doi.org/10.1063/1.2783426

**Emergence of singular structures in Oldroyd-B fluids.** / Thomases, Becca; Shelley, Michael.

Research output: Contribution to journal › Article

*Physics of Fluids*, vol. 19, no. 10, 103103. https://doi.org/10.1063/1.2783426

}

TY - JOUR

T1 - Emergence of singular structures in Oldroyd-B fluids

AU - Thomases, Becca

AU - Shelley, Michael

PY - 2007/10

Y1 - 2007/10

N2 - Numerical simulations reveal the formation of singular structures in the polymer stress field of a viscoelastic fluid modeled by the Oldroyd-B equations driven by a simple body force. These singularities emerge exponentially in time at hyperbolic stagnation points in the flow and their algebraic structure depends critically on the Weissenberg number. Beyond a first critical Weissenberg number the stress field approaches a cusp singularity, and beyond a second critical Weissenberg number the stress becomes unbounded exponentially in time. A local approximation to the solution at the hyperbolic point is derived from a simple ansatz, and there is excellent agreement between the local solution and the simulations. Although the stress field becomes unbounded for a sufficiently large Weissenberg number, the resultant forces of stress grow subexponentially. Enforcing finite polymer chain lengths via a FENE-P penalization appears to keep the stress bounded, but a cusp singularity is still approached exponentially in time.

AB - Numerical simulations reveal the formation of singular structures in the polymer stress field of a viscoelastic fluid modeled by the Oldroyd-B equations driven by a simple body force. These singularities emerge exponentially in time at hyperbolic stagnation points in the flow and their algebraic structure depends critically on the Weissenberg number. Beyond a first critical Weissenberg number the stress field approaches a cusp singularity, and beyond a second critical Weissenberg number the stress becomes unbounded exponentially in time. A local approximation to the solution at the hyperbolic point is derived from a simple ansatz, and there is excellent agreement between the local solution and the simulations. Although the stress field becomes unbounded for a sufficiently large Weissenberg number, the resultant forces of stress grow subexponentially. Enforcing finite polymer chain lengths via a FENE-P penalization appears to keep the stress bounded, but a cusp singularity is still approached exponentially in time.

UR - http://www.scopus.com/inward/record.url?scp=35748960853&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=35748960853&partnerID=8YFLogxK

U2 - 10.1063/1.2783426

DO - 10.1063/1.2783426

M3 - Article

VL - 19

JO - Physics of Fluids

JF - Physics of Fluids

SN - 1070-6631

IS - 10

M1 - 103103

ER -