1.5.1 1D Euler equations in conservation form

The Euler equations (2) restricted to one spatial dimension,

$${ \renewedcommand{arraystretch}{1.2} \frac{\partial }{\part... ...! \begin{array}{c} 0 \\ 0 \\ 0 \end{array} \! \right) }$$ (40)

have the form (conservation form)

$$\frac{\partial }{\partial t} \ensuremath{\mathchoice{\mbox{... ...th$\scriptstyle 0$}} {\mbox{\boldmath$\scriptscriptstyle 0$}}}$$ (41)

for the quantity vector $\ensuremath{\mathchoice{\mbox{\boldmath$\displaystyle q$... ...ox{\boldmath$\scriptstyle q$}} {\mbox{\boldmath$\scriptscriptstyle q$}}}$ with flux vector $\ensuremath{\mathchoice{\mbox{\boldmath$\displaystyle F$... ...ox{\boldmath$\scriptstyle F$}} {\mbox{\boldmath$\scriptscriptstyle F$}}}$,

$${ \renewedcommand{arraystretch}{1.2} \ensuremath{\mathchoic... ...+ \! P \right] \; v_{} \!\! \end{array} \right) \enspace . }$$ (42)