Integration Strategies for Efficient Multizone Chemical Kinetics Models

Three integration strategies are developed and tested for the stiff, ordinary differential equation (ODE) integrators used to solve the fully coupled multizone chemical kinetics model. Two of the strategies tested are found to provide more than an order of magnitude of improvement over the original, basic level of usage for the stiff ODE solver. One of the faster strategies uses a decoupled, or segregated, multizone model to generate an approximate Jacobian. This approach yields a 35-fold reduction in the computational cost for a 20 zone model. Using the same approximate Jacobian as a preconditioner for an iterative Krylov-type linear system solver, the second improved strategy achieves a 75-fold reduction in the computational cost for a 20 zone model. The faster strategies achieve their cost savings with no significant loss of accuracy. The pressure, temperature and major species mass fractions agree with the solution from the original integration approach to within six significant digits; and the radical mass fractions agree with the original solution to within four significant digits. The faster strategies effectively change the cost scaling of the multizone model from cubic to quadratic, with respect to the number of zones. As a consequence of the improved scaling, the 40 zone model offers more than a 250-fold cost savings over the basic calculation.