New Numerical Techniques for Some non-Newtonian Flow Models
Young-Ju Lee, Penn State

In this talk, we shall report a new discretization scheme in a unified framework for simulating various rate-type non-Newtonion fluid models. This scheme is shown to preserve some important physical characteristics of the fluids that is believed to be crucial for the numerical stability of any discretization scheme. This scheme is further enhanced by combining with grid adaptivity and multigrid solution techniques. Our new numerical schemes have been implemented to identify appropriate constitutive models for an interesting phenomenon observed in a lab experiment: unlike in any Newtonian fluid, a falling sphere through some non-Newtonian fluids does not reach its terminal velocity but it undergoes continual oscillations as it falls.