Efficient Computation for a Reaction-Diffusion System with a Fast Reaction in Two Spatial Dimensions Using COMSOL Multiphysics

Abstract

We study a reaction-diffusion system of three chemical species, where two chemicals react with a much faster rate than the other reaction in the model. We are interested in the asymptotic limit as the rate becomes in finite. This forces the reaction interface to have an asymptotically small width with asymptotically large height. Numerical simulations for the three species model with large reaction rate become progressively more challenging and costly as the singularity becomes sharper. But in the asymptotic limit, an equivalent two component model can be defined that is significantly cheaper computationally and allows for effective studies for the model. The equivalence is demonstrated by the analytical definition of the two component model and by comparing numerical results to ones for the three species model with progressively larger reaction rates, which also demonstrate the computational efficiency.