Peristaltic pumping by wavelike contractions is a fundamental
biomechanical mechanism for fluid and material transport and is used
in the esophagus, intestine, oviduct, and ureter. While peristaltic
pumping of a Newtonian fluid is well understood, in many important
settings, as in the fluid dynamics of reproduction, the fluids have
non-Newtonian responses. Here, I will present a numerical method for
simulating an Oldroyd-B fluid coupled to contractile, moving walls. A
marker and cell grid-based projection method is used for the fluid
equations and an immersed boundary method is used for coupling to a
Lagrangian representation of the deforming walls. We examine
numerically the peristaltic transport of a highly viscous Oldroyd-B
fluid over a range of Weissenberg numbers and peristalsis wavelengths
and amplitudes