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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 highlevels of numerical stiffness typically present in chemical kinetic modelsrelevant to transportation/power-generation applications make the efficientevaluation/factorization of the chemical kinetic Jacobian and thermochemicalsource-terms critical to the performance of reactive-flow codes. Here weinvestigate the performance of vectorized evaluation ofconstant-pressure/volume thermochemical source-term and sparse/dense chemicalkinetic Jacobians using single-instruction, multiple-data (SIMD) andsingle-instruction, multiple thread (SIMT) paradigms. These are implemented inpyJac, an open-source, reproducible code generation platform. A new formulationof the chemical kinetic governing equations was derived and verified, resultingin Jacobian sparsities of 28.6-92.0% for the tested models. Speedups of3.40-4.08x were found for shallow-vectorized OpenCL source-rate evaluationcompared with a parallel OpenMP code on an avx2 central processing unit (CPU),increasing to 6.63-9.44x and 3.03-4.23x for sparse and dense chemical kineticJacobian evaluation, respectively. Furthermore, the effect of data-ordering wasinvestigated and a storage pattern specifically formulated for vectorizedevaluation was proposed; as well, the effect of the constant pressure/volumeassumptions and varying vector widths were studied on source-term evaluationperformance. Speedups reached up to 17.60x and 45.13x for dense and sparseevaluation on the GPU, and up to 55.11x and 245.63x on the CPU over afirst-order finite-difference Jacobian approach. Further, dense Jacobianevaluation was up to 19.56x and 2.84x times faster than a previous version ofpyJac on a CPU and GPU, respectively.

Using SIMD and SIMT vectorization to evaluate sparse chemical kinetic Jacobian matrices and thermochemical source terms