The low Mach number flows typically encountered in combustion are characterized by strong density variations resulting from the change of composition and the heat released by numerous chemical reactions involving multiple chemical species. A highly scalable, high order code based on the open source computational fluid dynamics spectral element solver NEK5000 is used to integrate the conservation equations at this limit, employing a high-order splitting scheme. NEK5000 is designed to minimize memory access and workload by casting the main computational kernels in the form of localized highly-efficient matrix-matrix product routines. The solution of the discretized system is obtained through scalable parallel multigrid preconditioned conjugate gradient method with fast coarse-grid solvers. The code makes use of automated domain-decomposition techniques that ensure load balancing, efficient communication strategies for inter-element data exchange and parallel IO.
The chemical species and energy equations accounting for detailed chemistry and transport are integrated implicitly without further splitting using an efficient stiff ordinary differential equation solver (CVODE). The reactive solver which inherits the scalability and efficiency of NEK5000 has been used to perform numerical experiments on different setups of fundamental and applied interest, including instabilities of laminar non-premixed and premixed flames, non-catalytic and catalytic combustion in micro- and meso-scale channels, laminar and turbulent catalytic combustion and autoignition of diluted hydrogen jets in hot turbulent co- and cross-flowing air. Recent developments have enabled numerical experiments of flow, mixing and combustion in time-varying engine-like geometries.