In this post I am going to derive the compressible Euler equations: $latex \frac{\partial \rho}{\partial t} + \nabla \cdot (\rho \vec{V}) =0$ (1) $latex \rho \frac{\partial \vec{V}}{\partial t} + \rho \vec{V} \cdot \nabla \vec{V} = -\nabla p$ (2) $latex \rho \dot{q} = \frac{\partial}{\partial t}\rho e  + \nabla \cdot \left[\rho (h+\frac{|V|^2}{2})\right]$ (3) These equations are essentially … Continue reading Derivation of the Euler Equations