Preconditioned time differencing for stiff ODEs in diurnal atmospheric kinetics

The equations of atmospheric chemical kinetics are often very stiff. It is, in large part, due to the computational expense involved with solving these equations, that extended integrations of three-dimensional chemical-radiative-transport models are still not economically feasible. The problem with stiff equations is the severe limitation placed on the stepsize of an explicit scheme due to stability, which forces the use of an implicit scheme. The problem with the implicit scheme, however, is that a non-linear system must be solved at each step. In this paper, we examine a methodology that yields unconditionally stable, explicitly computable methods for a class of chemical kinetics equations without requiring the use of a Jacobian matrix. These methods are variants of a fixed point iterative method and are called preconditioned time differencing methods. We show that these methods are significantly faster than the counterpart methods in widespread use with chemical-radiative-transport models. This result lays the groundwork for further research that promises to significantly improve the performance of these vital research models.