  Galaxy cluster mergers are a powerful laboratory for testing cosmological and
astrophysical models. However, interpreting individual merging clusters depends
crucially on their merger configuration, defined by the masses, velocities,
impact parameters, and orientation of the merger axis with respect to the plane
of the sky. In this work, we investigate the impact of merger parameters on the
X-ray emitting intracluster medium and gravitational lensing maps using a suite
of idealised simulations of binary cluster mergers performed using the GAMER-2
code. As a test case, we focus on modeling the Bullet Cluster-like merging
system Abell 2146, in which deep \textit{Chandra} X-ray and lensing
observations revealed prominent merger shocks as well as the mass distribution
and substructures associated with this merging cluster. We identify the most
interesting parameter combinations, and evaluate the effects of various
parameters on the properties of merger shocks observed by deep \textit{Chandra}
and lensing observations. We show that due gravitational compression of the
cluster halos during the merger, previous mass estimates from weak lensing are
too high. The plane of the merger is tilted further from the plane of the sky
than estimated previously, up to $30^\circ$ from the plane of the sky. We
discuss the applicability of our results to multi-wavelength observations of
merging galaxy clusters and their use as probes of cosmology and plasma
physics.
