  Building a self-gravitating hydrodynamic code as a combination of a
hydrodynamic solver and a gravity solver is discussed. We show that
straightforward combining those two solvers generally leads to a code that does
not conserve energy locally, and instead a special Consistency Condition ought
to be satisfied. A particular example of combining Softened Lagrangian
Hydrodynamics (SLH) with a P3M gravity solver is used to demonstrate the effect
of the Consistency Condition for a self-gravitating hydrodynamic code. The need
to supplement the SLH method with the P3M gravity solver arose because the
Moving Mesh Gravity solver, used in conjunction with the SLH method previously,
was found to produce inaccurated results. We also show that most existing
cosmological hydrodynamic codes implicitly satisfy the Consistency Condition.
