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 that interact with CHs of different geometries, such as circular, elliptic, convex, and concave shapes. We analysed the effect of these geometries on the density profiles of the reflected waves, and we generated the corresponding simulation-based time-distance plots. Within these time-distance plots, we determined 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 will enable us to explain interaction parameters of the observed interaction events, such as the density structure of the reflected wave. These parameters are usually difficult to understand comprehensively based on an analysis of the measurements alone. Moreover, we show that the interaction between a concave CH and CWs, whose density profile includes an enhanced as well as a depleted wave part, can lead to reflected density amplitudes that are more than twice larger than the incoming density amplitudes. 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 that the choice of the path that is used to generate the time-distance plots is important and that this choice affects the interpretation of the CW-CH interaction results.