  Symmetry-preserving (mimetic) discretization aims to preserve certain
properties of a continuous differential operator in its discrete counterpart.
For these discretizations, stability and (discrete) conservation of mass,
momentum and energy are proven in the same way as for the original continuous
model.
  In our papers arXiv:1710.07149 and arXiv:1901.02264, we presented space
discretization schemes for various models, which had exact conservation of
mass, momentum and energy. Mass and momentum conservation followed from the
left null spaces of the discrete operators used. The conservation of energy in
the continuous and discrete models is more complicated, and the papers had
little space for their complete derivation. This paper contains the derivation
of the energy equations in more detail than was given in the papers
arXiv:1710.07149 and arXiv:1901.02264.
