Chapman Cycle Model

The actual computation of the time dependant results of the Chapman Cycle requires the use of a "stiff" equation solver. This means that the evolution of at least one type of molecule in the equations depends very strongly on small changes in another molecular concentration. The model used on page 1 solves for an equilibrium solution using a Newton-Rhapson method. This method, while both quick and accurate, does not tell the user how long it takes to establish equilibrium, nor does it give information on the stability of the solution. You might try using an initial guess for the O radical concentration which is greater than the molecular oxygen concentration. Notice that this gives the result of a completely atomic gas, an unstable equilibrium.

The time dependant results of a solution of the rate equations can be seen below.

(Harvey, E. and Sweeney, B., Modeling Stratospheric Ozone Kinetics, JCE Online 1999.)