  Rayleigh-Taylor instability is a classical hydrodynamic instability of great
interest in various disciplines of science and engineering, including
astrophyics, atmospheric sciences and climate, geophysics, and fusion energy.
Analytical methods cannot be applied to explain the long-time behavior of
Rayleigh-Taylor instability, and therefore numerical simulation of the full
problem is required. However, in order to capture the growth of amplitude of
perturbations accurately, both the spatial and temporal discretization need to
be extremely fine for traditional numerical methods, and the long-time
simulation may become prohibitively expensive. In this paper, we propose
efficient reduced order model techniques to accelerate the simulation of
Rayleigh-Taylor instability in compressible gas dynamics. We introduce a
general framework for decomposing the solution manifold to construct the
temporal domain partition and temporally-local reduced order model construction
with varying Atwood number. We propose two practical approaches in this
framework, namely decomposition by using physical time and penetration distance
respectively. Numerical results are presented to examine the performance of the
proposed approaches.
