Fluid-Structure Interaction for the Classroom: Interpolation, Hearts, and Swimming!

While students may find spline interpolation quite digestible based on their familiarity with the continuity of a function and its derivatives, some of its inherent value may be missed when they only see it applied to standard data interpolation exercises. In this paper, we offer alternatives in which students can qualitatively and quantitatively witness the resulting dynamical differences when objects are driven through a fluid using different spline interpolation methods. They say that seeing is believing; here we showcase the differences between linear and cubic spline interpolation using examples from fluid pumping and aquatic locomotion. Moreover, students can define their own interpolation functions and visualize the dynamics that unfold. To solve the fluid-structure interaction system, the open-source fluid dynamics software IB2d is used. In that spirit, all simulation codes, analysis scripts, and movies are provided for streamlined use.