PRISM: Piecewise reusable implementation of solution mapping. an economical strategy for chemical kinetics

In a chemical kinetics calculation, a solution-mapping procedure is applied to parametrize the solution of the initial-value ordinary differential equ ation system as a set of algebraic polynomial equations. To increase the ac curacy, the parametrization is done piecewise, dividing the multidimensiona l chemical composition space into hypercubes and constructing polynomials f or each hypercube. A differential equation solver is used to provide the so lution at selected points throughout a hypercube, and from these solutions the polynomial coefficients are determined. Factorial design methods are us ed to reduce the required number of computed points. The polynomial coeffic ients for each hypercube are stored in a data structure for subsequent reus e, since over the duration of a flame simulation it is likely that a partic ular set of concentrations and temperature will occur repeatedly at differe nt times and positions. The method is applied to H-2-air combustion using an 8-species reaction set . After N-2 is added as an inert species and enthalpy is considered, this r esults in a 10-dimensional chemical composition space. To add the capabilit y of using a variable time-step, time-step is added as an additional dimens ion, making an 11-dimensional space. Reactive fluid dynamical simulations o f a 1-D laminar premixed flame and a 2-D turbulent non-premixed jet are per formed. The results are compared to identical control runs which use an ord inary differential equation solver to calculate the chemical kinetic rate e quations. The resulting accuracy is very good, and a factor of 10 increase in computational efficiency is attained.