[Faculty] Fwd: [CSRC.COLLOQUIUM] "Proper Orthogonal Decomposition (POD) of the flow dynamics for a viscoelastic fluid in a four-roll mill geometry at the Stokes Limit"

[Jose Castillo]

<https://lh3.googleusercontent.com/-ZPFNPh16sR0/Wt39FrXUP-I/AAAAAAAAAaw/3wQunGe20lUopmV_ggfPaDwE9cVAgVzxgCLcBGAs/s1600/image001.jpg>

DATE:  *Friday, October 5, 2018*




TITLE:


*Proper Orthogonal Decomposition (POD) of the flow dynamics for a
viscoelastic fluid in a four-roll mill geometry at the Stokes Limit*




TIME:  *3:30PM*



LOCATION:  *GMCS 314*



SPEAKER/BIO:

*Paloma Gutierrez, *
*Krener Assistant Professor, *


*Department of Mathmetics, UC Davis *





ABSTRACT:

Numerical simulations of viscoelastic fluids in the Stokes limit with a
four-roll mill background force were performed at a range of Weissenberg
number (non-dimensional relaxation time). For small Weissenberg number the
flow is steady and symmetric but upon increasing the Weissenberg number
(corresponding to increased elasticity or flow memory time), the flow
becomes unstable leading to a variety of temporal evolutions to different
periodic and aperiodic solutions. These dynamics were analyzed using a
Proper Orthogonal Decomposition (POD) that extracted elastic modes in terms
of their contribution to the energy of the system. The temporal behavior of
the system, captured by the decomposition, indicates that the motion of the
stagnation points drives the different flow transitions. In particular, a
transition to an asymmetric state occurs when the extensional stagnation
points lose their pinning to the background forcing. A further transition
to higher frequency modal dynamics occurs when the stagnation points that
were initially tied by the forcing to the centers of the rolls, begin to
move. The relative frequencies of the motion of these stagnation points is
a critical factor in determining the complexity of the flow, measured by
the number of modes needed to capture most of the energy in the system.
Even when the flows are more complex a small number of modes is sufficient
to capture the time evolution of these flows, demonstrating the usefulness
of the POD applied to viscoelastic fluids at the Stokes limit.
  HOST:  Gustaaf Jacobs

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