  Aims: Bow shock waves are a common feature of groups and clusters of galaxies
since they are generated as a result of supersonic motion of galaxies through
the intergalactic medium. The goal of this work is to present an analytical
solution technique for such astrophysical hypersonic blunt body problems.
Methods: A method, developed by Schneider (1968, JFM, 31, 397) in the context
of aeronautics, allows calculation of the galaxy's shape as long as the shape
of the bow shock wave is known (so-called inverse method). In contrast to other
analytical models, the solution is valid in the whole flow region (from the
stagnation point up to the bow shock wings) and in particular takes into
account velocity gradients along the streamlines. We compare our analytical
results with two-dimensional hydrodynamical simulations carried out with an
extended version of the VH-1 hydrocode which is based on the piecewise
parabolic method with a Lagrangian remap. Results: It is shown that the applied
method accurately predicts the galaxy's shape and the fluid variables in the
post-shock flow, thus saving a tremendous amount of computing time for future
interpretations of similar objects. We also find that the method can be applied
to arbitrary angles between the direction of the incoming flow and the axis of
symmetry of the body. We emphasize that it is general enough to be applied to
other astrophysical bow shocks, such as those on stellar and galactic scales.
