The decoupled direct method for calculating sensitivity coefficients in chemical kinetics

Abstract

A version of the direct method for calculating first-order sensitivity coefficients is extended to nonlinear, time-dependent models defined by stiff differential equations. In this approach the auxiliary equations for the sensitivity coefficients are solved separately from the model equations. Accuracy and stability are maintained by using exactly the same time steps and numerical approximations in calculating the sensitivities as are used in calculating the model solution. The decoupling procedure also greatly increases the efficiency of the method by taking advantage of the fact that the auxiliary equations for different sensitivity coefficients are quite similar. The decoupled direct method is applied to stiff chemical mechanisms for the oxidation of hydrocarbons in the atmosphere, the pyrolysis of ethane, and the oxidation of formaldehyde in the presence of carbon monoxide. Sensitivity coefficients are also calculated for the three mechanisms by a method employing Green’s function and by actually varying the input parameters. Based on these results, the decoupled direct method has advantages in simplicity, stability, accuracy, efficiency, storage requirements, and program size over other methods, including those using Green’s function. Specifically, the decoupled direct method is as much as a factor of 6 more efficient than a recent version of the Green’s function method. Extensions of the decoupled direct method are also discussed.