Optimizing Time Integration of Chemical-Kinetic Networks for Speed and Accuracy

摘要

This paper describes enhancements to a sparse, adaptively-preconditioned, solver for chemical-kinetic ignition simulations. A concurrent submission [1] describes the adaptively preconditioned solver, showing orders of magnitude reduction in computational time for ignition delay calculations with large chemical mechanisms. Building on that solver implementation, this paper describes further improvements in three categories: 1) Fast vector exponentiation implemented in the Arrhenius and equilibrium rate constant calculations, 2) Fill-reducing matrix permutations for Jacobian factorization and back substitution, and 3) custom-code generation tailored to specific chemical mechanisms. A series of vector exponentials developed by other authors are implemented in the code and tested for speed and accuracy. The accuracy of the functions is tested against the standard library exponential function and for their affect on the accuracy of calculated ignition delay times. The fastest, high precision exponential is found to be from the Intel MKL library and provides approximately a nine times speed-up over the standard exponential on the system tested. Alternatively, an implementation with a permissive distribution license gives approximately an eight times speedup with acceptable accuracy. Fill-reducing matrix permutations are found to be an important factor governing matrix operation costs during time integration. We tested the COLAMD, MMD, Metis nested-dissection, and Reverse Cuthill-McKee methods. The SuperLU implementation of MMD was found to give the best permutations (minimizing matrix fill-in) for the chemical systems we investigated. Disabling diagonal pivoting in the permutation procedure further reduces the amount of fill-in. The custom-code generator is designed to create tailored source files for the calculation of rate constants and species production rates for chemical mechanisms. This allows an optimizing compiler to produce the most optimal machine code for a mechanism by reordering operations to increase cache locality and reduces the number of operations necessary by completely unrolling loops. Without these improvements the adaptively-preconditioned solver gives a 1600-fold reduction in computational time for ignition delay calculations with a 7172 species biodiesel mechanism (from 26 hours to under one minute). The improvements reported here provide an additional factor of two reduction in wall clock integration time for ignition delay calculations over a sweep of mechanism sizes from ten to 7172 species. For the 7172 species mechanism, ignition delay time is reduced to about 30 seconds, giving ～3000-fold speedup over the dense solver approach.