# Derivation of the Euler Equations

In this post I am going to derive the compressible Euler equations:

$\frac{\partial \rho}{\partial t} + \nabla \cdot (\rho \vec{V}) =0$ (1)

$\rho \frac{\partial \vec{V}}{\partial t} + \rho \vec{V} \cdot \nabla \vec{V} = -\nabla p$ (2)

$\rho \dot{q} = \frac{\partial}{\partial t}\rho e + \nabla \cdot \left[\rho (h+\frac{|V|^2}{2})\right]$ (3)

# Oblique Shockwaves

In this post I go over the theory of oblique shocks by building on our understand of normal shockwaves! I will give a short overview of the theory and strategy for analysis.

# Pressure Driven Nozzle Flow with Shock – rhoCentralFoam

In this post I will go over the set up and solution of a pressure driven nozzle flow with a shock located in the diverging section. This refers to the type of flow problem described by region b in my page covering stationary normal shock-waves.