Reduction of round-off errors in chemical kinetics

Abstract

In this paper, a modification of chemical kinetics is introduced in order to reduce round-off errors in stiff source terms. Fast chemical processes close to partial equilibrium are often composed of different contributions that cancel each other out (for example forward and backward reactions). These contributions tend to be very large compared to their sum. Thus, computer evaluation of the chemical source term can lead to serious round-off errors due to cancellation. This can cause severe convergence problems within Newton's method when simulating the process with implicit integration methods and thus lead to additional step size reduction. Here, a method is presented that reduces the round-off error by making a slight change to the model. Furthermore, this change is smooth and does not change the dimension, so that it is also possible to apply the method locally when solving partial differential equations. Numerical examples presented in this paper verify the approach.

Keywords:

• chemical kinetics
• Newton's method
• quasi-steady state assumption
• regularisation
• round-off error

Disclosure statement

No potential conflict of interest was reported by the authors.