Numerical approximation of a reaction-diffusion system with fast reversible reaction

TL;DR

This paper analyzes the finite volume approximation of a reaction-diffusion system with fast reversible reactions, proving convergence to a nonlinear diffusion problem independent of reaction kinetics.

Contribution

It establishes convergence of the finite volume scheme to the weak solution, including the limit as reaction rates tend to infinity, with kinetic-independent estimates.

Findings

Approximate solutions converge to the weak solution.

Solutions satisfy estimates independent of reaction speed.

Convergence to nonlinear diffusion problem as discretization refines.

Abstract

We consider the finite volume approximation of a reaction-diffusion system with fast reversible reaction. We deduce from a priori estimates that the approximate solution converges to the weak solution of the reaction-diffusion problem and satisfies estimates which do not depend on the chemical kinetics factor. It follows that the solution converges to the solution of a nonlinear diffusion problem, as the size of the volume elements and the time steps converge to zero while the kinetic rate tends to infinity.