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Abstract

The Navier-Stokes equations are used to model fluid flow. Examples include fluid structure interactions in the heart, climate and weather modeling, and flow simulations in computer gaming and entertainment. The equations date back to the 1800s, but research and development of numerical approximation algorithms continues to be an active area. To numerically solve the Navier-Stokes equations we implement a least squares finite element algorithm based on work by Roland Glowinski and colleagues. We use the deal.II academic library , the C++ language, and the Linux operating system to implement the solver. We investigate convergence rates and apply the least squares solver to the lid driven cavity problem and discuss results.

Author Bio

Taylor Boatwright is a mathematics major with minors in history and political science at Francis Marion University in Florence, SC, USA. She is the President of FMU Diplomats, Treasurer of Green Club, the Chair of the Budget Committee for Teaching Fellows, and lead Resident Assistant on campus. She plans to teach high school mathematics after graduating for a few years and then attend graduate school afterwards.

Ja’Nya Breeden studies Computer Science and Mathematics at Francis Marion University. After having experience with web development, she transitioned to learning software engineering and using mathematics to solve problems in engineering disciplines. She is the Chair of the Francis Marion ACM Student Chapter and Vice President of the Art Club and Math Club.

Jada Lytch is originally from Dillon, SC, USA. She is a mechanical engineering major at Francis Marion University in Florence, SC, USA. She is a member of the math club and the American Society of Mechanical Engineering. Her interests include applied mathematics and mechanics of materials. After graduating, she plans to attend graduate school.

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