Hyungeun Shin

Derivation of Navier-Stokes equation and CFD

In my final presentation, I present the derivation of Navier-Stokes equation, which is an interesting topic for engineers, physicists, and mathematicians. There may be different versions of deriving the equation, but my presentation will include an explanation in a perspective of physics as much as possible. Before deriving the equation, continuity equation will be explained, which corresponds to material derivative. The Navier-Stokes equation is derived in Eulerian description which explain some physical transport with a concept of control volume. Then, I will introduce computational fluid dynamics about various topics such as turbulence and multiphase in order to show people things in which mathematicians may be interested.