A mathematical model for the sulphur dioxide aggression to calcium carbonate stones: Numerical approximation and asymptotic analysis

被引：40
作者：
Aregba-Driollet, D
Diele, F
Natalini, R
机构：
[1] Univ Bordeaux 1, Math Appl Bordeaux, F-33405 Talence, France
[2] CNR, Ist Applicaz Calcolo M Picone, Sez Bari, I-70126 Bari, Italy
[3] CNR, Ist Applicaz Calcolo M Picone, I-00161 Rome, Italy
来源：
SIAM JOURNAL ON APPLIED MATHEMATICS | 2004年 / 64卷 / 05期
关键词：
chemical aggression; porous media; nonlinear parabolic equations; fast reaction limit; free boundary problems; finite element; finite differences;
D O I：
10.1137/S003613990342829X
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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 veri. cation of this asymptotics is given. Our results are in qualitative agreement with the experimental behavior observed in the chemical literature.
引用
收藏
页码：1636 / 1667
页数：32
相关论文
共 27 条
[1]  
ALI G, 2004, NUMERICAL QUALITATIV
[2]  
Amoroso G.G., 1983, Stone Decay and Conservation
[3]  
[Anonymous], 2003, 19 IAC
[4]  
Barenblatt GI, 1990, THEORY FLUID FLOWS N
[5]  
Belhadj M, 2003, ASYMPTOTIC ANAL, V34, P41
[6]   Rate of formation of black crusts on marble. A case study [J].
Bugini, Roberto ;
Tabasso, Marisa Laurenzi ;
Realini, Marco .
JOURNAL OF CULTURAL HERITAGE, 2000, 1 (02) :111-116
[7]  
GARBASSI F, 1985, DURABILITY BUILDING, V3, P51
[8]  
Gauri K. l., 1982, DURAB BUILD MAT, V1, P209
[9]  
GAURI KL, 1982, DURABILITY BUILD MAT, V1, P217
[10]   Strong stability-preserving high-order time discretization methods [J].
Gottlieb, S ;
Shu, CW ;
Tadmor, E .
SIAM REVIEW, 2001, 43 (01) :89-112
123