Section: New Results

Numerical simulation of concrete carbonation

In [20], C. Chainais-Hillairet, B. Merlet, and A. Zurek introduce and study a Finite Volume scheme for a concrete carbonation model proposed by Aiki and Muntean in [50]. This 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 scheme is obtained by a Euler discretization in time and a Scharfetter–Gummel discretization in space. The convergence of the scheme is established and the existence of a solution to the model is obtained as a by-product. Finally, some numerical experiments are performed to show the efficiency of the scheme.

In [45], A. Zurek studies the long-time regime of the moving interface appearing in the concrete carbonation model. He proves that the approximate free boundary, given by an implicit-in-time Finite Volume scheme, increases in time following a $\sqrt{t}$-law. This result is illustrated by numerical experiments.