An explicit time-integration framework for accelerated direct numerical simulations of stiff reacting flows

The computational singular perturbation (CSP) solver potentially allows significant acceleration of high-fidelity simulations of reacting flows with detailed chemistry by eliminating the fast timescales in explicit time integration. The partitioning of the fast and slow timescales is achieved through the evaluation of Jacobian eigenstructures, which has been recognized as a major performance bottleneck for computational efficiency. This study presents a way to resolve the computational overhead by employing an adaptive binned-state hash (BSH) mapping which allows the reuse of Jacobian eigenstructures throughout the entire simulation. The strategy bypasses conventional hash-table collision handling, thus preserving adaptivity and scalability for parallel computing algorithms. The CSP-BSH solver is implemented in the high-order KAUST Adaptive Reacting Flow Solver (KARFS), and its performance is compared against the benchmark stiff implicit solver CVODE in simulations of a two-dimensional (2D) laminar flame–vortex interaction and a three-dimensional (3D) flame–turbulence interaction with a detailed ammonia/air reaction mechanism. The results demonstrate the accuracy and robustness of the reuse of Jacobian eigenstructures for unsteady simulations. The BSH mapping reduces the computational overhead of the CSP solver from 75% to about 10%, with the mapping itself introducing only 1% overhead, enabling up to seven-fold speedup compared to CVODE, even with a moderate size of the kinetic mechanism.