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Abstract Accurately predicting key combustion phenomena in reactive-flow simulations, e.g., lean blow-out, extinction/ignition limits and pollutant formation, necessitates the use of detailed chemical kinetics. The large size and high levels of numerical stiffness typically present in chemical kinetic models relevant to transportation/power-generation applications make the efficient evaluation/factorization of the chemical kinetic Jacobian and thermochemical source-terms critical to the performance of reactive-flow codes. Here we investigate the performance of vectorized evaluation of constant-pressure/volume thermochemical source-term and sparse/dense chemical kinetic Jacobians using single-instruction, multiple-data (SIMD) and single-instruction, multiple thread (SIMT) paradigms. These are implemented in pyJac, an open-source, reproducible code generation platform. Selected chemical kinetic models covering the range of sizes typically used in reactive-flow simulations were used for demonstration. A new formulation of the chemical kinetic governing equations was derived and verified, resulting in Jacobian sparsities of 28.6–92.0% for the tested models. Speedups of 3.40–4.08 × were found for shallow-vectorized OpenCL source-rate evaluation compared with a parallel OpenMP code on an avx2 central processing unit (CPU), increasing to 6.63–9.44 × and 3.03–4.23 × for sparse and dense chemical kinetic Jacobian evaluation, respectively. Furthermore, the effect of data-ordering was investigated and a storage pattern specifically formulated for vectorized evaluation was proposed; as well, the effect of the constant pressure/volume assumptions and varying vector widths were studied on source-term evaluation performance. Speedups reached up to 17.60 × and 45.13 × for dense and sparse evaluation on the GPU, and up to 55.11 × and 245.63 × on the CPU over a first-order finite-difference Jacobian approach. Further, dense Jacobian evaluation was up to 19.56 × and 2.84 × times faster than a previous version of pyJac on a CPU and GPU, respectively. Finally, future directions for vectorized chemical kinetic evaluation and sparse linear-algebra techniques were discussed. [ABSTRACT FROM AUTHOR]

A fifth-order implicit Runge–Kutta method and two fourth-order exponential integration methods equipped with Krylov subspace approximations were implemented for the GPU and paired with the analytical chemical kinetic Jacobian software pyJac . The performance of each algorithm was evaluated by integrating thermochemical state data sampled from stochastic partially stirred reactor simulations and compared with the commonly used CPU-based implicit integrator CVODE . We estimated that the implicit Runge–Kutta method running on a single Tesla C2075 GPU is equivalent to CVODE running on 12–38 Intel Xeon E5-4640 v2 CPU cores for integration of a single global integration time step of 10 − 6 s with hydrogen and methane kinetic models. In the stiffest case studied—the methane model with a global integration time step of 10 − 4 s —thread divergence and higher memory traffic significantly decreased GPU performance to the equivalent of CVODE running on approximately three CPU cores. The exponential integration algorithms performed more slowly than the implicit integrators on both the CPU and GPU. Thread divergence and memory traffic were identified as the main limiters of GPU integrator performance, and techniques to mitigate these issues were discussed. Use of a finite-difference Jacobian on the GPU—in place of the analytical Jacobian provided by pyJac —greatly decreased integrator performance due to thread divergence, resulting in maximum slowdowns of 7.11 − 240.96 × ; in comparison, the corresponding slowdowns on the CPU were just 1.39 − 2.61 × , underscoring the importance of use of an analytical Jacobian for efficient GPU integration. Finally, future research directions for working towards enabling realistic chemistry in reactive-flow simulations via GPU/SIMT accelerated stiff chemical kinetics integration were identified. [ABSTRACT FROM AUTHOR]

The relative importance index (RII) method for determining appropriate target species for dynamic adaptive chemistry (DAC) simulations using the directed relation graph with error propagation (DRGEP) method is developed. The adequacy and effectiveness of this RII method is validated for two fuels: n-heptane and isopentanol, representatives of a ground transportation fuel component and bio-alcohol, respectively. The conventional method of DRGEP target species selection involves picking an unchanging (static) set of target species based on the combustion processes of interest; however, these static target species may not remain important throughout the entire combustion simulation, adversely affecting the accuracy of the method. In particular, this behavior may significantly reduce the accuracy of the DRGEP-based DAC approach in complex multidimensional simulations where the encountered combustion conditions cannot be known a priori with high certainty. Moreover, testing multiple sets of static target species to ensure the accuracy of the method is generally computationally prohibitive. Instead, the RII method determines appropriate DRGEP target species solely from the local thermo-chemical state of the simulation, ensuring that accuracy will be maintained. Further, the RII method reduces the expertise required of users to select DRGEP target species sets appropriate to the combustion phenomena under consideration. Constant volume autoignition simulations run over a wide range of initial conditions using detailed reaction mechanisms for n-heptane and isopentanol show that the RII method is able to maintain accuracy even when traditional static target species sets fail, and are even more accurate than expert-selected target species sets. Additionally, the accuracy and efficiency of the RII method are compared to those of static target species sets in single-cell engine simulations under homogeneous charge compression ignition conditions. For simulations using more stringent DRGEP thresholds, the RII method performs similarly to that of the static target species sets. With a larger DRGEP threshold, the RII method is significantly more accurate than the static target species sets without imposing significant computational overhead. Furthermore, the applicability of the RII method to a DRG-based DAC scheme is discussed. [ABSTRACT FROM AUTHOR]