Computational Economy Improvements in PRISM

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.