Gas dynamic tests

The Euler equations for an ideal gas in 2D are

U_t + F(U)_x + G(U)_y = 0,

where

$$U = \left( \begin{array}{l} \rho\\ \rho u \\ \rho v \\ \rho E... ...rho u v \\ \rho v^2 + p \\ v (\rho E + p) \end{array} \right).$$

Here $\rho$ is the density, u the velocity in the x-direction, v the velocity in the y direction, E=e+1/2 (u²+v²) is the total energy, e is the internal energy density, and $p=(\gamma -1)\rho e$is the pressure.