High-order algorithms for compressible reacting flow with complex chemistry

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 options for fourth order to eighth order in time. The implementation uses a hybrid programming model designed for effective utilisation 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.