Numerical methods for the solution of large kinetic systems Original Research Article

The photochemical reaction mechanisms used in air pollution models usually consider 40 to 100 pollutant species and more than 150 reactions. The equations resulting from these chemical mechanisms are nonlinear, highly coupled and extremely stiff depending on the time of the day. Therefore, the simulation time of the models is determined to a large degree by the computational burden associated with the solution of the chemistry equations. In recent years, the Quasi Steady State Approximation (QSSA) method is favored for solving the chemistry equations. In the QSSA the solution of large linear systems is not necessary. In this paper we investigate a new approach based on the BDF which solves the sparse linear equations during the Newton iteration by linear Gauss-Seidel iterations. The Jacobian is computed explicitly and not by finite differences. The effect of different numbers of Gauss-Seidel sweeps is investigated. In addition, sparsing techniques proposed by Nowak (1992) and Zlatev (1991) are tested with respect to their efficiency in our algorithms. Our method is compared with respect to its accuracy as well as computational speed with a method of Verwer (1993) which is also based on the two-step BDF combined with nonlinear Gauss-Seidel iterations to approximately determine the implicitly defined solution. The results show that our BDF code reaches the nonlinear Gauss-Seidel approach of Verwer (1993) with respect to the computational speed.