Numerical optimization methods within a continuation strategy for the reduction of chemical combustion models

Abstract

Model reduction methods in chemical kinetics are used for simplification of models which involve a number of different time scales. Slow invariant manifolds in chemical composition space are supposed to be identified. A selection of state variables serve for parametrization of these manifolds. Species reconstruction methods are used to compute the values of the remaining variables in dependence of the parameters. We discuss theoretical results and numerical methods for an application of a model reduction method that is developed by D. Lebiedz based on optimization of trajectories. The main focus of this work is an application of the model reduction method to models of chemical combustion. The existence of a solution of the semi-infinite optimization problem, which has to be solved to obtain a local approximation of the slow manifold, is proven. A finite optimization problem for the same purpose is presented which can be solved with a generalized Gauss-Newton method. This method is used with an active set strategy. A filter framework and iterations with second order correction are employed for globalization of convergence. Families of neighboring optimization problems can be solved efficiently in a predictor corrector continuation scheme. The tangent space of the slow manifold can be computed by evaluation of sensitivity equations for the parametric optimization problem. A step size strategy is applied in the continuation scheme for efficient progress along the homotopy path. Results of an application of the presented method are shown and discussed. The test models range from simple test examples to realistic models of syngas combustion in air.