MATH481

This course will focus on the mathematical modeling of fluid flows through and around organs and organisms, with an emphasis on topics of current medical and environmental interest. The natural world is replete with examples of cells, organs, and organisms whose shape influences flow to their benefit. For example, the shape of a maple seed generates lift which allows them to disperse farther. The design of the aortic valve prevents backflow during ventricular refilling while reducing disturbed regions of flow. The structure of a coral reef enhances the uptake of nutrients and the removal of wastes. A barracudas body shape reduces drag and allows it to quickly accelerate. In this course, we will mathematically describe the shape of organisms using 3D computer aided design (CAD). We will then use computational and experimental fluid dynamics to resolve the flow around 3D printed physical and numerical models. Mathematical topics will include the use of differential equations to describe fluid flow, numerical solutions of differential equations, image analysis, and the use of computational fluid dynamics software.

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