  Large-scale simulations of time-dependent problems generate a massive amount
of data and with the explosive increase in computational resources the size of
the data generated by these simulations has increased significantly. This has
imposed severe limitations on the amount of data that can be stored and has
elevated the issue of input/output (I/O) into one of the major bottlenecks of
high-performance computing. In this work, we present an in situ compression
technique to reduce the size of the data storage by orders of magnitude. This
methodology is based on time-dependent subspaces and it extracts low-rank
structures from multidimensional streaming data by decomposing the data into a
set of time-dependent bases and a core tensor. We derive closed-form evolution
equations for the core tensor as well as the time-dependent bases. The
presented methodology does not require the data history and the computational
cost of its extractions scales linearly with the size of data -- making it
suitable for large-scale streaming datasets. To control the compression error,
we present an adaptive strategy to add/remove modes to maintain the
reconstruction error below a given threshold. We present four demonstration
cases: (i) analytical example, (ii) incompressible unsteady reactive flow,
(iii) stochastic turbulent reactive flow, and (iv) three-dimensional turbulent
channel flow.
