Computationally efficient implementation of combustion chemistry in parallel PDF calculations

In parallel calculations of combustion processes with realistic chemistry, the serial in situ adaptive tabulation (ISAT) algorithm [S.B. Pope, Computationally efficient implementation of combustion chemistry using in situ adaptive tabulation, Combustion Theory and Modelling, 1 (1997) 41–63; L. Lu, S.B. Pope, An improved algorithm for in situ   adaptive tabulation, Journal of Computational Physics 228 (2009) 361–386] substantially speeds up the chemistry calculations on each processor. To improve the parallel efficiency of large ensembles of such calculations in parallel computations, in this work, the ISAT algorithm is extended to the multi-processor environment, with the aim of minimizing the wall clock time required for the whole ensemble. Parallel ISAT strategies are developed by combining the existing serial ISAT algorithm with different distribution strategies, namely purely local processing (PLP), uniformly random distribution (URAN), and preferential distribution (PREF). The distribution strategies enable the queued load redistribution of chemistry calculations among processors using message passing. They are implemented in the software x2f_mpix2f_mpi, which is a Fortran 95 library for facilitating many parallel evaluations of a general vector function. The relative performance of the parallel ISAT strategies is investigated in different computational regimes via the PDF calculations of multiple partially stirred reactors burning methane/air mixtures. The results show that the performance of ISAT with a fixed distribution strategy strongly depends on certain computational regimes, based on how much memory is available and how much overlap exists between tabulated information on different processors. No one fixed strategy consistently achieves good performance in all the regimes. Therefore, an adaptive distribution strategy, which blends PLP, URAN and PREF, is devised and implemented. It yields consistently good performance in all regimes. In the adaptive parallel ISAT strategy, the type and extent of redistribution is determined “on the fly” based on the prediction of future simulation time. Compared to the PLP/ISAT strategy where chemistry calculations are essentially serial, a speed-up factor of up to 30 is achieved. The study also demonstrates that the adaptive strategy has acceptable parallel scalability.