  In this paper we describe a numerical algorithm for integrating the
multicomponent, reacting, compressible Navier-Stokes equations, targeted for
direct numerical simulation of combustion phenomena. The algorithm addresses
two shortcomings of previous methods. First, it incorporates an eighth-order
narrow stencil approximation of diffusive terms that reduces the communication
compared to existing methods and removes the need to use a filtering algorithm
to remove Nyquist frequency oscillations that are not damped with traditional
approaches. The methodology also incorporates a multirate temporal integration
strategy that provides an efficient mechanism for treating chemical mechanisms
that are stiff relative to fluid dynamical time scales. The overall methodology
is eighth order in space with option for fourth order to eighth order in time.
The implementation uses a hybrid programming model designed for effective
utilization of many-core architectures. We present numerical results
demonstrating the convergence properties of the algorithm with realistic
chemical kinetics and illustrating its performance characteristics. We also
present a validation example showing that the algorithm matches detailed
results obtained with an established low Mach number solver.
