Gas Dynamics for Compressible Flow
The Kelvin-Helmholtz instability phenomenon occurs when there is a velocity difference between two fluids with different densities. This simulation shows the instabily of the interface between the two fluids.
\(
\frac{\partial \rho}{\partial t} + \nabla \cdot
\begin{bmatrix}
\rho u \\
\rho v \\
\end{bmatrix} = 0
\)
\(
\frac{\partial \rho u}{\partial t} + \nabla \cdot
\begin{bmatrix}
\rho u^2 + p \\
\rho u v \\
\end{bmatrix} = 0
\)
\(
\frac{\partial \rho v}{\partial t} + \nabla \cdot
\begin{bmatrix}
\rho u v \\
\rho v^2 + p \\
\end{bmatrix} = 0
\)
\(
\frac{\partial \rho E}{\partial t} + \nabla \cdot
\begin{bmatrix}
u(\rho E + p) \\
v(\rho E + p) \\
\end{bmatrix} = 0
\)
