| 1 | | Under construction |
| | 1 | The non-homogenous 1D Euler equations with self-gravity are given by |
| | 2 | |
| | 3 | [[latex($\frac{\partial }{\partial t} \begin{pmatrix} \rho \\ \rho u \\ E\end{pmatrix} + \frac{\partial }{\partial x} \begin{pmatrix} \rho u \\ \rho u^2 + p \\ u(E+p) \end{pmatrix} = \begin{pmatrix} 0 \\ - \rho \triangledown \phi_g \\ -\rho u \cdot \triangledown \phi_g \end{pmatrix}$)]] |
| | 4 | |
| | 5 | which in short hand notation is |
| | 6 | |
| | 7 | [[latex($\vec{u}_t + \vec{F}(\vec{u})_x = \vec{S}(\vec{u})$)]] |
| | 8 | |
| | 9 | where [[latex($\vec{u}$)]] is vector of fluid variables, [[latex($\vec{F}$)]] is their fluxes, and [[latex($\vec{S}$)]] is the source-term vector. |
| | 10 | |
