  We present numerical studies of wetting on various topographic substrates,
including random topographies. We find good agreement with recent predictions
based on an analytical interface-displacement-type theory
\cite{Herminghaus2012, Herminghaus2012a}. The phase diagrams are qualitatively
as predicted, but differently in this study the critical points are found to
lie within the physical parameter range (i.e., at positive contact angle) in
all cases studied. Notably, it is corroborated that Gaussian random surfaces
behave qualitatively different from all non-Gaussian topographies investigated,
exhibiting a qualitatively different phase diagram. This shows that Gaussian
random surfaces must be used with great care in the context of wetting
phenomena.
