Efficient Computation for a Reaction-Diffusion System with a Fast Reaction with Continuous and Discontinuous Initial Data Using COMSOL Multiphysics

Abstract

In a chemical reaction-diffusion system with three species, the interaction between diffusion and a fast reaction between two species creates a transient, sharp, internal interface. Besides the three species model, we use a two component model that is equivalent in the asymptotic limit as the reaction becomes infinitely fast. We use COMSOL Multiphysics for the simulations and use the time-dependent analysis of the general form of the problem for accurate representation of derivatives of the non-linear terms. For a representative continuous initial condition, detailed comparisons of results in one spatial dimension confirm that the two component model is the asymptotic limit of the three species model, but is significantly more numerically efficient. Additional studies in both one and two spatial dimensions confirm that COMSOL Multiphysics obtains the same steady state solution also for several initial conditions with jump discontinuities.