  The expanding ejecta of supernova remnants (SNRs) are believed to form dust
in dense clumps of gas. Before the dust can be expelled into the interstellar
medium and contribute to the interstellar dust budget, it has to survive the
reverse shock that is generated through the interaction of the preceding
supernova blast wave with the surrounding medium. The conditions under which
the reverse shock hits the clumps change with remnant age and define the dust
survival rate. To study the dust destruction in the SNR Cassiopeia A, we
conduct magnetohydrodynamical simulations of the evolution of a supernova blast
wave and of the reverse shock. In a second step we use these evolving
conditions to model clumps that are disrupted by the reverse shock at different
remnant ages. Finally, we compute the amount of dust that is destroyed by the
impact of the reverse shock. We find that most of the dust in the SNR is hit by
the reverse shock within the first 350 yr after the SN explosion. While the
dust destruction in the first 200 yr is almost complete, we expect greater dust
survival rates at later times and almost total survival for clumps that are
first impacted at ages beyond 1000 yr. Integrated over the entire evolution of
the SNR, the dust mass shows the lowest survival fraction (17 per cent) for the
smallest grains (1 nm) and the highest survival fraction (28 per cent) for the
largest grains (1000 nm).
