The PRISM piecewise solution mapping procedure is applied to reactive flow simulations of (9–species) H2+air combustion. PRISM takes the solution of the chemical kinetic ODE system and parameterizes it with quadratic polynomials. To increase the accuracy, the parameterization is done piecewise, by dividing the multi-dimensional chemical composition space into hypercubes and constructing polynomials for each hypercube on demand. The polynomial coefficients are stored for subsequent repeated reuse. Initial cost of polynomial construction is expensive, but it recouped as the hypercube is reused, hence computational gain depends on the degree of hypercube reuse. We present two methods that help us to identify hypercubes that will ultimately have high reuse, this being accomplished before the expense of constructing polynomials has been incurred. One method utilizes the rate of movement of the chemical trajectory to estimate the number of steps the trajectory would make through the hypercube. The other method defers polynomial construction until a preset threshold of reuse has been met; an empirical method which, nevertheless, produces a substantial gain. The methods are tested on a 0-D chemical mixture and reactive flow 1 and 2-D simulations of selected laminar and turbulent H2+air flames. The computational performance of PRISM is improved by a factor of about 2 for both methods.
BT - International Journal of Chemical Kinetics C2 - LBNL-48858 DA - 05/2003 N2 -The PRISM piecewise solution mapping procedure is applied to reactive flow simulations of (9–species) H2+air combustion. PRISM takes the solution of the chemical kinetic ODE system and parameterizes it with quadratic polynomials. To increase the accuracy, the parameterization is done piecewise, by dividing the multi-dimensional chemical composition space into hypercubes and constructing polynomials for each hypercube on demand. The polynomial coefficients are stored for subsequent repeated reuse. Initial cost of polynomial construction is expensive, but it recouped as the hypercube is reused, hence computational gain depends on the degree of hypercube reuse. We present two methods that help us to identify hypercubes that will ultimately have high reuse, this being accomplished before the expense of constructing polynomials has been incurred. One method utilizes the rate of movement of the chemical trajectory to estimate the number of steps the trajectory would make through the hypercube. The other method defers polynomial construction until a preset threshold of reuse has been met; an empirical method which, nevertheless, produces a substantial gain. The methods are tested on a 0-D chemical mixture and reactive flow 1 and 2-D simulations of selected laminar and turbulent H2+air flames. The computational performance of PRISM is improved by a factor of about 2 for both methods.
PY - 2003 SP - 438 EP - 452 T2 - International Journal of Chemical Kinetics TI - Computational Economy Improvements in PRISM VL - 35 ER -