A Mathematical Model for the Sulphur Dioxide Aggression to Calcium Carbonate Stones: Numerical Approximation and Asymptotic Analysis
Authors:
- D. Aregba-DriolletDAD. Aregba-Driollet
- F. DieleFDF. Diele
- R. NataliniRNR. Natalini
- 1 January 2004
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Applied Mathematics
- Vol. 64 (5) , 1636-1667
Abstract
We introduce a degenerate nonlinear parabolic system that describes the chemical aggression of calcium carbonate stones under the attack of sulphur dioxide. For this system, we present some finite element and finite difference schemes to approximate its solutions. Numerical stability is given under suitable CFL conditions. Finally, by means of a formal scaling, the qualitative behavior of the solutions for large times is investigated, and a numerical verification of this asymptotics is given. Our results are in qualitative agreement with the experimental behavior observed in the chemical literature.Keywords
This publication has 14 references indexed in Scilit:
- Weathering and damageJournal of Geophysical Research: Solid Earth, 2002
- Strong Stability-Preserving High-Order Time Discretization MethodsSIAM Review, 2001
- Nonlinear diffusion in the presence of fast reactionNonlinear Analysis, 2000
- Rate of formation of black crusts on marble. A case studyJournal of Cultural Heritage, 2000
- The Fast Reaction Limit for a Reaction-Diffusion SystemJournal of Mathematical Analysis and Applications, 1996
- A non-linear theory of high-concentration-gradient dispersion in porous mediaAdvances in Water Resources, 1995
- The Stefan Problem1992
- Rate of Decay of Marble in Laboratory and Outdoor ExposureJournal of Materials in Civil Engineering, 1989
- Kinetics of Reaction of SO2 with MarbleJournal of Materials in Civil Engineering, 1989
- Atmospheric damage to calcareous stones: Comparison and reconciliation of recent experimental findingsAtmospheric Environment (1967), 1989