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Physical Sciences and Mathematics Commons

Open Access. Powered by Scholars. Published by Universities.®

Mathematics

Smith College

2019

Oldroyd-B

Articles 1 - 2 of 2

Full-Text Articles in Physical Sciences and Mathematics

Convergent Solutions Of Stokes Oldroyd-B Boundary Value Problems Using The Immersed Boundary Smooth Extension (Ibse) Method, David B. Stein, Robert D. Guy, Becca Thomases Jun 2019

Convergent Solutions Of Stokes Oldroyd-B Boundary Value Problems Using The Immersed Boundary Smooth Extension (Ibse) Method, David B. Stein, Robert D. Guy, Becca Thomases

Mathematics Sciences: Faculty Publications

The Immersed Boundary (IB) method has been widely used to solve fluid-structure interaction problems, including those where the structure interacts with polymeric fluids. In this paper, we examine the convergence of one such scheme for a well known two-dimensional benchmark flow for the Oldroyd-B constitutive model, and we show that the traditional IB-based scheme fails to adequately capture the polymeric stress near to embedded boundaries. We analyze the reason for such failure, and we argue that this feature is not specific to the case study chosen, but a general feature of such methods due to lack of convergence in velocity …


Proper Orthogonal Decomposition (Pod) Of The Flow Dynamics For A Viscoelastic Fluid In A Four-Roll Mill Geometry At The Stokes Limit, Paloma Gutierrez-Castillo, Becca Thomases Feb 2019

Proper Orthogonal Decomposition (Pod) Of The Flow Dynamics For A Viscoelastic Fluid In A Four-Roll Mill Geometry At The Stokes Limit, Paloma Gutierrez-Castillo, Becca Thomases

Mathematics Sciences: Faculty Publications

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 …