  The geometry of a coronal hole (CH) affects the density profile of the
reflected part of an incoming global coronal wave (CW). In this study, we
perform for the first time magnetohydrodynamic (MHD) simulations of fast-mode
MHD waves interacting with CHs of different geometries, such as circular,
elliptic, convex, and concave shapes. We analyse the influence these geometries
have on the density profiles of the reflected waves and we generate the
corresponding simulation-based time-distance plots. Within these time-distance
plots we determine regions that exhibit specific density features, such as
large reflected density amplitudes. In a further step, these interaction
features can be compared to actual observed CW-CH interaction events which
makes it possible to explain interaction parameters from the observed
interaction events, such as the density structure of the reflected wave, which
are usually difficult to comprehensively understand by only analysing the
measurements. Moreover, we show that the interaction between a concave shaped
CH and CWs, whose density profile include an enhanced as well as a depleted
wave, can lead to reflected density amplitudes that are more than two times
larger than the incoming ones. Another effect of the interplay between the
constructive and destructive interference of the reflected wave parts is a
strongly depleted region in the middle of the CW-CH interaction process. In
addition, we show how important the choice of the path is that is used to
generate the time-distance plots and how this choice affects the interpretation
of the CW-CH interaction results.
