Numerical simulation of moving immersed bodies in fluids is now practiced routinely. A variety of variants of these approaches have been published, most of which rely on using a background mesh for the fluid equations and tracking the body using Lagrangian points. In this talk, generalized constraint–based governing equations will be presented that provide a unified framework for various immersed body techniques. The governing equations are developed so that they are independent of the nature of temporal or spatial discretization schemes. Application of this technique to interrogate aquatic locomotion will be discussed. Specifically, an example of convergent evolution will be presented where we found that a very diverse group of aquatic animals use a particular mechanically optimal method of swimming that has evolved independently at least eight times in both vertebrate and invertebrate swimmers. We have also derived a new efficiency measure called the energy consumption coefficient, which is a non-dimensional measure of energy consumption. This metric is a fundamental metric to quantify efficiency of self-propelled bodies analogous to the drag coefficient to quantify aerodynamic shapes of vehicles. Our analysis leads to allometric scalings of frequency and velocity of swimming and flying organisms over more than twenty orders of magnitude of mass.

Bio:
Neelesh Patankar received his BS (B.Tech.) in Mechanical Engineering from the Indian Institute of Technology, Bombay (1993) and his doctorate in Mechanical Engineering from the University of Pennsylvania (1997). Following his Ph.D., he was a post-doctoral associate with Prof. Daniel D. Joseph at the University of Minnesota until 2000. He joined the Department of Mechanical Engineering at Northwestern University in 2000. Neelesh is a Fellow of the American Physical Society. He has received the NSF CAREER award, the International Conference on Multiphase Flow's Junior Award that is given once in three years, and has been one of seventeen academicians selected to the Defense Science Study Group in 2010. Neelesh is on the Editorial Boards of the Journal of Computational Physics. He is on the Advisory Board of the International Journal of Multiphase Flow. Neelesh has also received several teaching awards including the best teacher award in the School of Engineering at Northwestern University (2013).