  We compute an analog Casimir effect in a one-dimensional spinless Luttinger
liquid confined to a segment in the presence of a nearly-impenetrable partition
dividing the segment into two compartments. The Casimir interaction is found to
be a bounded piecewise-continuous oscillatory function whose maxima are points
of force discontinuity and correspond to resonant tunneling across the
partition. The well-known regularization-based results are reproduced by the
lower envelope of this function, which corresponds to an approximation that
ignores the rather large oscillations due to particle discreteness. These
macroscopic conclusions are tested and confirmed via a rigorous analysis of the
Casimir effect in an exactly-solvable model of a one-dimensional
non-relativistic spinless gas of free fermions, thus resolving an objection
that has been raised by Volovik (2003).
  Additionally we confirm the result of a recent calculation which employed an
effective low-energy theory with a cutoff to find the Casimir interaction
between two strong well-separated impurities placed in a Luttinger liquid.
