Computing positive stable numerical solutions of moving boundary problems for concrete carbonation

This paper deals with the construction and computation of numerical solutions of a coupled mixed partial differential equation system arising in concrete carbonation problems. The moving 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. In fact, positivity of the concentrations, increasing properties of the propagation front and monotone behavior of the solution are proved. We also confirm numerically the t-law of propagation. Results are illustrated with numerical examples.