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

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...

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Veröffentlicht in:Combustion and flame Jg. 198; S. 186 - 204
Hauptverfasser: Curtis, Nicholas J., Niemeyer, Kyle E., Sung, Chih-Jen
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York Elsevier Inc 01.12.2018
Elsevier BV
Schlagworte:
Central processing units
Chemical kinetics
Computer simulation
CPUs
Finite difference method
Ignition limits
Jacobi matrix method
Jacobian
Jacobians
Kinetics
Mathematical analysis
Matrix
Matrix methods
Organic chemistry
Performance evaluation
Pressure effects
Reaction kinetics
SIMD
SIMD (computers)
SIMT
Simulation
Sparse
Sparsity
Stiffness
Sparse
Jacobian
SIMD
SIMT
Chemical kinetics
ISSN:0010-2180, 1556-2921
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Zusammenfassung: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.
Bibliographie:ObjectType-Article-1
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ISSN:0010-2180
1556-2921
DOI:10.1016/j.combustflame.2018.09.008