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October 1984

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40

Comparison of Numerical Techniques for Integration of Stiff Ordinary

Differential Equations Arising in Combustion Chemistry

Krishnan Radhakrishnan

Chemical kinetics; Stiff ordinary differential equations; Numerical solution

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A03

Krishnan Radhakrishnan, University of Michigan, Ann Arbor, Michigan (work partially funded by NASA grants

NAG3–147 and NAG3–294), and National Research Council—NASA Research Associate.

The efficiency and accuracy of several algorithms recently developed for the efficient numerical integration of stiff

ordinary differential equations are compared. The methods examined include two general-purpose codes, EPISODE and

LSODE, and three codes (CHEMEQ, CREK1D, and GCKP84) developed specifically to integrate chemical kinetic rate

equations. The codes are applied to two test problems drawn from combustion kinetics. The comparisons show that

BODE is the fastest code currently available for the integration of combustion kinetic rate equations. An important

finding is that an interactive solution-of the algebraic energy conservation equation to compute the temperature does not

result in significant errors. In addition, this method can be more efficient than evaluating the temperature by integrating

its time derivative. Significant reductions in computational work are realized by updating the rate constants (k = ATN

exp(–E/RT)) only when the temperature change exceeds an amount ∆T that is problem dependent. An approximate

expression for the automatic evaluation of ∆T is derived and is shown to result in increased efficiency.