  Numerical simulations have played a vital role in the design of modern
combustion systems. Over the last two decades, the focus of research has been
on the development of the large eddy simulation (LES) approach, which leveraged
the vast increase in computing power to dramatically improve predictive
accuracy. Even with the anticipated increase in supercomputing capabilities,
the use of LES in design is limited by its high computational cost. Moreover,
to aid decision making, such LES computations have to be augmented to estimate
underlying uncertainties in simulation components. At the same time, other
changes are happening across industries that build or use combustion devices.
While efficiency and emissions reduction are still the primary design
objectives, reducing cost of operation by optimizing maintenance and repair is
becoming an important segment of the enterprise. This latter quest is aided by
the digitization of combustors, which allows collection and storage of
operational data from a host of sensors over a fleet of devices. Moreover,
several levels of computing including low-power hardware present on board the
combustion systems are becoming available. Such large data sets create unique
opportunities for design and maintenance if appropriate numerical tools are
made available. As LES revolutionized computing-guided design by leveraging
supercomputing, a new generation of numerical approaches is needed to utilize
this vast amount of data and the varied nature of computing hardware. In this
article, a review of emerging computational approaches for this heterogeneous
data-driven environment is provided. A case is made that new but unconventional
opportunities for physics-based combustion modeling exist in this realm.
