Solving Moving Boundary Concrete Carbonation Models

Abstract

In this work we present a finite difference method to solve a coupled mixed partial differential equation system arising in concrete carbonation problems. The free boundary problem under study is firstly transformed in a fixed boundary one, allowing the computation of the propagation front as a new unknown that can be computed together with the mass concentrations of CO2 in air and water. Apart from the stability and the consistency of the numerical solution, constructed by a finite difference scheme, qualitative properties of the numerical solution are established without proof. In fact, positivity of the concentrations, increasing properties of the propagation front and monotone behaviour of the solution are proved. We also confirm numerically the t-law of propagation.