PRISM: Piecewise Reusable Implementation of Solution Mapping. An Economical Strategy for Chemical Kinetics

Abstract

AbstractIn a chemical kinetics calculation, a solution‐mapping procedure is applied to parametrize the solution of the initial‐value ordinary differential equation system as a set of algebraic polynomial equations. To increase the accuracy, the parametrization is done piecewise, dividing the multidimensional chemical composition space into hypercubes and constructing polynomials for each hypercube. A differential equation solver is used to provide the solution at selected points throughout a hypercube, and from these solutions the polynomial coefficients are determined. Factorial design methods are used to reduce the required number of computed points. The polynomial coefficients for each hypercube are stored in a data structure for subsequent reuse, since over the duration of a flame simulation it is likely that a particular set of concentrations and temperature will occur repeatedly at different times and positions.The method is applied to H2–air combustion using an 8‐species reaction set. After N2 is added as an inert species and enthalpy is considered, this results in a 10‐dimensional chemical composition space. To add the capability of using a variable time‐step, time‐step is added as an additional dimension, making an 11‐dimensional space. Reactive fluid dynamical simulations of a 1‐D laminar premixed flame and a 2‐D turbulent non‐premixed jet are performed. The results are compared to identical control runs which use an ordinary differential equation solver to calculate the chemical kinetic rate equations. The resulting accuracy is very good, and a factor of 10 increase in computational efficiency is attained.