Uncoupling Techniques for Multispecies Diffusion–Reaction Model

Abstract

We consider the multispecies model described by a coupled system of diffusion–reaction equations, where the coupling and nonlinearity are given in the reaction part. We construct a semi-discrete form using a finite volume approximation by space. The fully implicit scheme is used for approximation by time, which leads to solving the coupled nonlinear system of equations at each time step. This paper presents two uncoupling techniques based on the explicit–implicit scheme and the operator-splitting method. In the explicit–implicit scheme, we take the concentration of one species in coupling term from the previous time layer to obtain a linear uncoupled system of equations. The second approach is based on the operator-splitting technique, where we first solve uncoupled equations with the diffusion operator and then solve the equations with the local reaction operator. The stability estimates are derived for both proposed uncoupling schemes. We present a numerical investigation for the uncoupling techniques with varying time step sizes and different scales of the diffusion coefficient.