  As modern hydrodynamic codes increase in sophistication, the availability of
realistic test problems becomes increasingly important. In gas dynamics, one
common unrealistic aspect of most test problems is the ideal gas assumption,
which is unsuited to many real applications, especially those involving high
pressure and speed metal deformation. Our work considers the collapsing cavity
and converging shock test problems, showing to what extent the ideal gas
assumption can be removed from their specification. It is found that while most
materials simply do not admit simple (i.e. scaling) solutions in this context,
there are infinite-dimensional families of materials which do admit such
solutions. We characterize such materials, derive the appropriate ordinary
differential equations, and analyze the associated nonlinear eigenvalue
problem. It is shown that there is an inherent tension between boundedness of
the solution, boundedness of its derivatives, and the entropy condition. The
special case of a constant-speed cavity collapse is considered and found to be
heuristically possible, contrary to common intuition. Finally, we give an
example of a concrete non-ideal collapsing cavity scaling solution based on a
recently proposed pseudo-Mie-Gruneisen equation of state.
