New Integration Techniques for Chemical Kinetic Rate Equations: Part II—Accuracy Comparison

A comparison of the accuracy of several techniques recently developed for solving stiff differential equations is presented. The techniques examined include two general-purpose codes EPISODE and LSODE developed for an arbitrary system of ordinary differential equations, and three specialized codes CHEMEQ, CREK1D, and GCKP84 developed specifically to solve chemical kinetic rate equations. The accuracy comparisons are made by applying these solution procedures to two practical combustion kinetics problems. Both problems describe adiabatic, homogeneous, gas-phase chemical reactions at constant pressure, and include all three combustion regimes: induction, heat release, and equilibration. The comparisons show that LSODE is the most efficient code—in the sense that it requires the least computational work to attain a specified accuracy level—currently available for chemical kinetic rate equations. An important finding is that an iterative solution of the algebraic enthalpy conservation equation for the temperature can be more accurate and efficient than computing the temperature by integrating its time derivative.