Computational economy improvements in PRISM

Abstract

The Piecewise Reusable Implementation of Solution Mapping (PRISM) procedure is applied to reactive flow simulations of (9-species) H₂ + air combustion. PRISM takes the solution of the chemical kinetic ordinary differential equation system and parameterizes it with quadratic polynomials. To increase the accuracy, the parameterization is done piecewise, by dividing the multidimensional 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-D 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. © 2003 Wiley Periodicals, Inc.^† Int J Chem Kinet 35: 438–452, 2003