I want to simulate a flow using the Euler equations. For this reason I'm wondering if there's a modified version of the Euler equations.
At the moment my formula looks like this:
$$ \frac{\partial}{\partial t} \begin{pmatrix} \rho \\ \rho v_1 \\ \rho v_2 \\ \rho v_3 \\ \rho E \end{pmatrix} = -\mathrm{div} \begin{pmatrix} \rho v_1 & \rho v_2 & \rho v_3 \\ \rho v_1^2 + p & \rho v_1 v_2 & \rho v_1 v_3 \\ \rho v_2 v_1 & \rho v_2^2 + p & \rho v_2 v_3 \\ \rho v_3 v_1 & \rho v_3 v_2 & \rho v_3^2 + p \\ (\rho E + p) v_1 & (\rho E + p) v_2 & (\rho E + p) v_3 \end{pmatrix} $$
Since the state variables are all in combination with the density, I need a division to calculate the flow. So what I actually would like to get is something like this:
$$ \frac{\partial}{\partial t} \begin{pmatrix} \rho \\ v_1 \\ v_2 \\ v_3 \\ E \end{pmatrix} $$
Can someone help?
