  We revisit the mesoscopic hydrodynamic description of the dynamics of sessile
compound drops, i.e., of drops that consist of two immiscible nonvolatile
partially wetting liquids and are situated on a smooth rigid solid substrate.
We briefly discuss and complete existing models employing a gradient dynamics
approach. Basing the underlying free energy on capillarity and wettability
contributions for all relevant interfaces in their full-curvature variant we
establish transparent consistency relations between macroscopic and mesoscopic
parameters. In consequence, we obtain mesoscopic Neumann and Young laws that
are also fully consistent with the macroscopic ones. In particular, we discuss
the minimal requirements for the wetting energy that ensure the full spectrum
of macroscopic parameters is addressed by the mesoscopic model. Having
established the dynamic model in long-wave and full-curvature variants, the
latter is employed to illustrate the usage of the mesoscopic model. As
examples, we use the spreading of individual compound drops on one-dimensional
horizontal substrates, sliding compound drops on one-dimensional inclined
substrates, and the coarsening of drop ensembles on one- and two-dimensional
horizontal substrates. In each case, the discussion emphasizes occurring
qualitative changes in the drop configurations.
