Convergence of a finite volume scheme for a parabolic system with a free boundary modeling concrete carbonation

Claire Chainais-Hillairet (1) , Benoît Merlet (1) , Antoine Zurek (1)

1 RAPSODI - Reliable numerical approximations of dissipative systems

In this paper we define and study a finite volume scheme for a concrete carbonation model proposed by Aiki and Muntean in [1]. The model consists in a system of two weakly coupled parabolic equations in a varying domain whose length is governed by an ordinary differential equation. The numerical sheme is obtained by a Euler discretisation in time and a Scharfetter-Gummel discretisation in space. We establish the convergence of the scheme. As a by-product, we obtain existence of a solution to the model. Finally, some numerical experiments show the efficiency of the scheme.

Mots clés: finite volume scheme; carbonation model; convergence analysis; free-boundary system

Domaines: Analyse numérique [math.NA]

Claire Chainais-Hillairet, Benoît Merlet, Antoine Zurek. Convergence of a finite volume scheme for a parabolic system with a free boundary modeling concrete carbonation. 2017. ⟨hal-02922751v1⟩