Direct and adjoint sensitivity analysis of chemical kinetic systems with KPP: II—numerical validation and applications

Abstract

The Kinetic PreProcessor KPP was extended to generate the building blocks needed for the direct and adjoint sensitivity analysis of chemical kinetic systems. An overview of the theoretical aspects of sensitivity calculations and a discussion of the KPP software tools is presented in the companion paper. In this work the correctness and efficiency of the KPP generated code for direct and adjoint sensitivity studies are analyzed through an extensive set of numerical experiments. Direct-decoupled Rosenbrock methods are shown to be cost-effective for providing sensitivities at low and medium accuracies. A validation of the discrete–adjoint evaluated gradients is performed against the finite difference estimates. The accuracy of the adjoint gradients is measured using a reference gradient value obtained with a standard direct-decoupled method. The accuracy is studied for both constant step size and variable step size integration of the forward/adjoint model and the consistency between the discrete and continuous adjoint models is analyzed. Applications of the KPP-1.2 software package to direct and adjoint sensitivity studies, variational data assimilation, and parameter identification are considered for the comprehensive chemical mechanism SAPRC-99.