Development of an Automatic Reduction Tool for Chemical Mechanisms and an Optimized Sparse Matrix Solver for Systems of Differential and Algebraic Equations

Abstract
An N-Heptane mechanism and a Methane/Propane mechanism have been reduced by an Automatic Reduction Tool (ART) and simulated with two different solver combinations, which solve the set of ordinary differential equations governing the time evolution of the species simultaneously with solving algebraic equations for species that can be considered to be in quasi steady state. The most successful of the two solver combinations is an optimized combination of Newton solvers. The algebraic part of the solver is based on a Newton solver and is given a speed-up by using the fact that the sparseness pattern of the Jacobian is constant in time. This allows for automatically written source code and an optimization of the sparseness pattern in a preprocessing step. The optimization method is based on a simulated annealing procedure that minimizes the number of operations in the algebraic part of the solver. The speed-up of the Newton solver for the algebraic equations is one of the major developments presented in this thesis. The other one is the development of the ART and the reduction of the N-Heptane and the Methane/Propane mechanisms using the ART.
A reduction down to 37 out of 110 species and 23 out of 118 species is achieved for the N-Heptane and Methane/Propane mechanism respectively, while the accuracy of the solution is maintained and the CPU time is significantly lower than that of the detailed mechanism. Less, but still greatly reduced mechanisms are generated for larger ranges of physical conditions.
Also, the two solver combinations were implemented into a commercial Computational Fluid Dynamics (CFD) code. CFD simulations were then performed for a detailed and reduced mechanism. The implementation involving the optimized combination of Newton solvers resulted in a speed-up for the reduced mechanism compared to the detailed mechanism, while the accuracy of important species for the reduced mechanism was well within acceptable limits.