  Explaining the observed diversity of supernovae (SNe) and the physics of
explosion requires knowledge of their progenitor stars, which can be obtained
by constraining the circumstellar medium (CSM). Models of the SN ejecta
colliding with CSM are necessary to infer the structure of the CSM and tie it
back to a progenitor model. Recent SNe I revealed CSM concentrated at a
distance $r\sim10^16$ cm, for which models of SN interaction are extremely
limited. In this paper, we assume the concentrated region is a "wall"
representing swept-up material, and unswept material lies outside the wall. We
simulate one-dimensional hydrodynamics of SNe Ia & Ib impacting 300 unique CSM
configurations using RT1D, which captures the Rayleigh-Taylor instability. We
find that the density ratio between the wall and ejecta -- denoted $A_0$ or
"wall height" -- is key, and higher walls deviate more from self-similar
evolution. Functional fits accounting for $A_0$ are presented for the forward
shock radius evolution. We show that higher walls have more degeneracy between
CSM properties in the deceleration parameter, slower shocks, deeper-probing
reverse shocks, slower shocked ejecta, less ejecta mass than CSM in the shock,
and more mixing of ejecta into the CSM at early times. We analyze observations
of SN 2014C (Type Ib) and suggest that it had a moderately high wall ($10 < A_0
< 200$) and wind-like outer CSM. We also postulate an alternate interpretation
for the radio data of SN 2014C, that the radio rise occurs in the wind rather
than the wall. Finally, we find that hydrodynamic measurements at very late
times cannot distinguish the presence of a wall, except perhaps as an
anomalously wide shock region.
