  The key role that dust plays in the interstellar medium has motivated the
development of numerical codes designed to study the coupled evolution of dust
and gas in systems such as turbulent molecular clouds and protoplanetary discs.
Drift between dust and gas has proven to be important as well as numerically
challenging. We provide simple benchmarking problems for dusty gas codes by
numerically solving the two-fluid dust-gas equations for steady, plane-parallel
shock waves. The two distinct shock solutions to these equations allow a
numerical code to test different forms of drag between the two fluids, the
strength of that drag and the dust to gas ratio. We also provide an
astrophysical application of J-type dust-gas shocks to studying the structure
of accretion shocks onto protoplanetary discs. We find that two-fluid effects
are most important for grains larger than 1 um, and that the peak dust
temperature within an accretion shock provides a signature of the dust-to-gas
ratio of the infalling material.
