  Advection driven problems are known to be difficult to model with a reduced
basis because of a slow decay of the Kolmogorov $N$-width. This paper
investigates how this challenge transfers to the context of solidification
problems and tries to answer when and to what extend reduced order models
(ROMs) work for solidification problems. In solidification problems, the
challenge is not the advection per se, but rather a moving solidification
front. This paper studies reduced spaces for 1D step functions that move in
time, which can either be seen as advection of a quantity or as a moving
solidification front. Furthermore, the reduced space of a 2D solidification
test case is compared with the reduced space of an alloy solidification
featuring a mushy zone. The results show that not only the PDE itself, but the
smoothness of the solution is crucial for the decay of the singular values and
thus the quality of a reduced space representation.
