Abstract

This thesis studies the incompressible Navier--Stokes equations from both theoretical and computational perspectives. On the analytical side, it develops the functional framework needed for weak formulations, including Sobolev spaces, weak derivatives, and variational methods, and uses these tools to discuss existence and uniqueness results for related partial differential equations. On the computational side, it implements a finite volume method for the two-dimensional lid-driven cavity problem. Numerical experiments are presented for different Reynolds numbers and grid resolutions, and the results are analyzed through streamline plots, velocity magnitude contours, divergence errors, and self-convergence tests. Together, these analytical and numerical components provide an introduction to the mathematical structure of incompressible flow and to practical methods for approximating its solutions.

Advisor

Bush, Michael

Department

Mathematics

Disciplines

Analysis | Numerical Analysis and Computation | Partial Differential Equations

Keywords

Incompressible Navier–Stokes equations, weak formulation, steady two-dimensional flow, Sobolev spaces, weak derivatives, Lax–Milgram theorem, Galerkin method, existence and uniqueness, finite volume method, lid-driven cavity flow.

Publication Date

2026

Degree Granted

Bachelor of Arts

Document Type

Senior Independent Study Thesis

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