Editing Appendix/Ramblings/HybridSchemeOld (section)

===Example #1===
This is certainly the most familiar component set.
<div align="center">
<table border="0" cellpadding="3">

<tr>
  <td align="right">
<math>\boldsymbol{\hat{e}}_x: ~~~\frac{\partial (\rho v_x)}{\partial t} + \nabla\cdot[(\rho v_x) \vec{v}~]</math>
  </td>
  <td align="center">
<math>~=~</math>
  </td>
  <td align="left">
<math>
-~\frac{\partial P}{\partial x} - \rho \frac{\partial \Phi}{\partial x} \, ,
</math>
  </td>
</tr>

<tr>
  <td align="right">
<math>\boldsymbol{\hat{e}}_y: ~~~\frac{\partial (\rho v_y)}{\partial t} + \nabla\cdot[(\rho v_y) \vec{v}~]</math>
  </td>
  <td align="center">
<math>~=~</math>
  </td>
  <td align="left">
<math>
-~\frac{\partial P}{\partial y} - \rho \frac{\partial \Phi}{\partial y} \, ,
</math>
  </td>
</tr>

<tr>
  <td align="right">
<math>\boldsymbol{\hat{e}}_z: ~~~\frac{\partial (\rho v_z)}{\partial t} + \nabla\cdot[(\rho v_z) \vec{v}~]</math>
  </td>
  <td align="center">
<math>~=~</math>
  </td>
  <td align="left">
<math>
-~\frac{\partial P}{\partial z} - \rho \frac{\partial \Phi}{\partial z} \, ,
</math>
  </td>
</tr>
</table>
</div>
where, for any one of the three scalar PDEs, advection of the relevant component of the momentum density, <math>~\psi_i</math>, is handled via the operation,

<div align="center">
<table border="0" cellpadding="3">
<tr>
  <td align="right">
<math>
\nabla\cdot[\psi_{i} \vec{v} ] 
</math>
  </td>
  <td align="center">
<math>~=~</math>
  </td>
  <td align="left">
<math>
\frac{\partial (\psi_i v_x)}{\partial x} + \frac{\partial (\psi_i v_y)}{\partial y} + \frac{\partial (\psi_i v_z)}{\partial z} \, .
</math>
  </td>
</tr>
</table>
</div>