Mathematical Biology Seminar Aaron Barrett, UNC Chapel Hill Wednesday, Jan. 23, 2019 3:05pm in LCB 225 An Adaptive Viscoelastic Fluid Solver: A Mucous Manifesto Abstract: Many fluids in the body exhibit non-Newtonian responses to stresses, and as such, the Navier-Stokes equations are inadequate to properly model these fluids. To model these polymeric, visco-elastic fluids, we often turn to Oldroyd-B type models where the immersed polymers are modeled using a linear Hooke's law for the restoring force. However, theory for how these models behave is severely lacking, and even getting numerical simulations to converge remains a significant challenge. In this talk, we present an overview of complex polymeric fluids by describing some of the challenges that arise with different fluid models as well as introducing a new adaptive method to overcome these challenges. We apply this new method to both classical benchmark problems and modelling bacterial locomotion.