Fluid-Structure Interaction for the Classroom: Speed, Accuracy, Convergence, and Jellyfish!

TL;DR

This paper introduces classroom activities using fluid-structure interaction modeling, including jellyfish locomotion, to teach convergence, accuracy, and computational efficiency in numerical methods.

Contribution

It provides practical activities and open-source tools to help students understand the balance between accuracy and computational resources in numerical analysis.

Findings

Convergence plots help illustrate accuracy versus practicality.

Different schemes can show varying convergence rates.

Error definitions influence convergence analysis.

Abstract

When is good, good enough? This question lingers in approximation theory and numerical methods as a competition between accuracy and practicality. Numerical Analysis is traditionally where the rubber meets the road: students begin to use numerical algorithms to compute approximate solutions to non-trivial problems. However, it is difficult for students to understand that more accuracy is not always the goal, but rather enough accuracy for practical use and meaningful interpretation. This compromise between accuracy and computational time/resources can be explored through the use of convergence plots. We offer a variety of classroom activities that allow students to discover the usefulness of convergence plots, including a contemporary example involving jellyfish locomotion using fluid-structure interaction modeling. These examples will additionally illustrate subtleties of convergence analysis: the same numerical scheme can exhibit different convergence rates, and the definition of `error' may change the convergence properties. To solve the fluid-structure interaction system, the open source software IB2d is used. All numerical codes, scripts, and movies are provided for streamlined integration into a classroom setting.