Numerical approximation of a concrete carbonation model: study of the $\sqrt{t}$-law of propagation

Antoine Zurek (1, 2)

1 LPP - Laboratoire Paul Painlevé - UMR 8524
2 RAPSODI - Reliable numerical approximations of dissipative systems

In this paper, we are interested in the long time behavior of approximate solutions to a free boundary model which appears in the modeling of concrete carbonation [1]. In particular, we study the long time regime of the moving interface. The numerical solutions are obtained by an implicit in time and finite volume in space scheme. We show the existence of solutions to the scheme and, following [2, 3], we prove that the approximate free boundary increases in time following a $\sqrt{t}$-law. Finally, we supplement the study through numerical experiments.

Domaines: Analyse numérique [math.NA]

Antoine Zurek. Numerical approximation of a concrete carbonation model: study of the $\sqrt{t}$-law of propagation. Numerical Methods for Partial Differential Equations, 2019, 35 (5), pp.1801-1820. ⟨10.1002/num.22377⟩. ⟨hal-01839277v2⟩