2.1 Basic Equations

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2.1 Basic Equations

So far, this section demonstrates only how nicely L^ATEX can display formulae...

The 3D hydrodynamics equations, including source terms due to gravity, are the mass conservation equation

$\begin{displaymath} \frac{\partial \rho}{\partial t} + \frac{\partial \; \rho \... ...frac{\partial \; \rho \; v{\rm 2}}{\partial x3} = 0 \enspace , \end{displaymath}$

(1)

the momentum equation

$\begin{displaymath} \frac{\partial }{\partial t} \left( \! \begin{array}{c} ... ...\rho \; g{\rm 2} \\ \rho \; g{\rm 3} \end{array} \! \right) \end{displaymath}$

(2)

and the energy equation

$\begin{displaymath} \frac{\partial \rho e{\rm ik}}{\partial t} + \frac{\partial... ... \; v{\rm 1} + g{\rm 2} \; v{\rm 2} + g{\rm 3} \; v{\rm 3} ) . \end{displaymath}$

(3)

In addition, there are equations for the 3D tensor viscosity and the non-local radiation transport.