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Dissolving stretchable polymers in a Newtonian (i.e. ordinary) fluid can give the fluid a new property called viscoelasticity.  Viscoelastic fluids exhibit fascinating behaviors due to the feedback force created by stretched polymers trying to return to their original length.   These fluids come with many mathematical challenges, including both numerical difficulties and open questions about the dynamics of flows.  

 

This talk will consist of 2 parts:  The first will relate to numerical methods and will introduce what we call the Double Immersed Boundary (DIB) method.  This is a modification of the existing Immersed Boundary (IB) method, which is very useful for simulating fluid-structure interactions, but cannot achieve convergence of the velocity gradients at boundaries, which are of particular importance to viscoelastic fluid simulations.  The DIB method remedies this problem for the special case where solutions are only required on one side of the boundary.  Naturally, there are tradeoffs, and the DIB method leads to interesting conditioning and stability issues that can be addressed in a variety of ways. 

 

The second part of the talk will relate more directly to fluid dynamics.  Viscoelastic fluids, even with high viscosity (i.e. zero Reynolds number), can exhibit chaotic behavior known as elastic turbulence.  This shares many features of Newtonian turbulence, but is a distinct and poorly understood phenomenon.  In particular, finding a dynamical origin or clear “route to chaos” has not been previously achieved for viscoelastic fluids.  We have carried out simulations of 2D viscoelastic Kolmogorov flow and found such a route.  An initial instability in Kolmogorov flow generates traveling wave solutions, which in turn lose stability as elasticity is increased.  Oscillations in the traveling waves emerge, which proceed through a period doubling cascade and eventually become chaotic.  Finding this route to chaos represents an exciting step towards understanding instabilities, chaos, and mixing in viscoelastic fluids, which has many applications in both industry and biology. 

Hybrid: Here's a zoom link: https://ucdavis.zoom.us/j/9167659477