Wolting, Ties (2026) The Euler Equations through Discrete Exterior Calculus. Bachelor's Thesis, Mathematics.
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Abstract
The Euler equations are a set of non-linear coupled partial differential equations arising in classical fluid mechanics, which describe the flow of non-viscous fluids. Due to their complicated nature, numerical solutions to the equations suffer from instabilities. In this thesis, we explore novel methods to deal with such instabilities. We introduce the notion of a fluid algebra, which describes velocity fields of fluid flow in a largely algebraic manner. Afterwards, we discuss the transverse intersection algebra (TIA), which is a combinatorial analogue of continuous exterior calculus. We apply a fluid algebra structure on the TIA to obtain a system of ordinary differential equations (ODEs), which approximate the Euler equations. Finally, we implement the geometric elements of the TIA in Python. Using this implementation, we apply it to the corresponding fluid algebra in order to numerically obtain and solve the system of ODEs approximating the Euler equations.
| Item Type: | Thesis (Bachelor's Thesis) |
|---|---|
| Supervisor name: | Veen, R.I. van der and Dimastrogiovanni, E. |
| Degree programme: | Mathematics |
| Thesis type: | Bachelor's Thesis |
| Language: | English |
| Date Deposited: | 03 Jul 2026 13:39 |
| Last Modified: | 03 Jul 2026 13:39 |
| URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/37328 |
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