Mathematics Colloquia and Seminars

Return to Colloquia & Seminar listing

Understanding the behavior of complex fluids in biology presents mathematical, modeling, and computational challenges not encountered in classical fluid mechanics, particularly, in the case of fluids with large elastic forces that interact with immersed elastic structures. We discuss some of the characteristics of strongly elastic flows and introduce different models and methods designed for these types of flows. We describe contributions from analysis that motivate numerical methods and illustrate their performance on different models on a simple test problem. Because biological problems often involve the coupled dynamics of active elastic structures and the surrounding fluid, we briefly introduce the immersed boundary method which has been used extensively for problems in Newtonian fluids. The methodology extends naturally to complex fluids in conjunction with the algorithms described earlier in this talk. We focus on implicit-time methods because the large elastic stresses in complex fluids necessitate high spatial resolution and long-time simulations. As an example to highlight some of the challenges of strongly elastic flows, we use the immersed boundary method to simulate an undulatory swimmer in a viscoelastic fluid using a data-based model for the prescribed shape.