Hohoi (Christ) Lin | 2026 I.S. Symposium
Name: Hohoi (Christ) Lin
罢颈迟濒别:听Analysis and Finite Volume Simulation of the Two-Dimensional Incompressible Navier-Stokes Equations
惭补箩辞谤蝉:听Mathematics; Business Economics
Advisors: Michael Bush; Huiting Tian
Fluid motion appears everywhere in daily life, from air moving around a room to water flowing in a river and blood circulating through the body. My Independent Study focuses on the Navier鈥揝tokes equations, one of the central mathematical models for describing these motions. What drew me to this project is that it connects rigorous mathematics with visible physical behavior: it asks both how we can understand fluid flow theoretically and how we can simulate it computationally. In three dimensions, the Navier鈥揝tokes equations are also connected to one of the Clay Millennium Problems, which makes the subject especially exciting.
In this project, I focused on the two-dimensional incompressible case, where the theory is better understood. On the analytical side, I developed the weak-solution framework needed to study existence and uniqueness for the steady problem. On the computational side, I implemented a finite volume method for the lid-driven cavity problem, a standard benchmark in computational fluid dynamics. The numerical results showed that increasing the Reynolds number changes the flow structure, while refining the computational grid makes the same structure clearer and better resolved.
What excites me most about this work is seeing how abstract ideas from analysis lead to concrete pictures of fluid motion. One conclusion I drew is that theory and computation are most powerful when used together: the mathematics explains why the model is meaningful, while the numerics show how it behaves in practice. A natural next step would be to compare my solver with established benchmark data and improve the code so it can automatically detect when the flow has effectively reached a steady state.
Posted in Symposium 2026 on May 1, 2026.
