Simulation of Chemical Kinetics Transport in the Stratosphere

Abstract

It is well known that the chemical rate equations are often very stiff and their numerical solutions must be treated quite carefully. At the present this does not present any major difficulty due to the class of special methods for stiff ordinary differential equations. However, in the simulation of chemical kinetics transport in the stratosphere and related fields we are faced with a large system of stiff partial differential equations. Abstractly we may write the equations as

$$ \frac{{\partial y}}{{\partial t}} = T\left( y \right) + C\left( y \right), $$

((1))

where y is a vector representing the concentrations of the chemical species and t is simply time. T is a linear partial differential operator describing the mass transfer of the chemical species [Colgrove (1965A), Gudiksen (1968A)]†. C is a highly nonlinear chemical kinetics operator involving not only the concentrations of these species but also some complicated integrals of these concentrations [Crutzen (1971A), Johnston (1971A)]. The physical problem is usually formulated either as an initial-boundary value problem or simply as a boundary value problem $\left( {i.e.\frac{{\partial y}} {{\partial t}} = 0} \right).$.

Work performed in part under the auspices of the U. S. Atomic Energy Commission and in part supported by the Climatic Impact Assessment Program, Office of the Secretary, Dept. of Transportation