Moving carbonation fronts in concrete: A moving-sharp-interface approach

a b s t r a c tThis paper deals with the construction and computation of numerical solutions of a coupled mixed partial differential equation system arising in concrete carbonation problems. The moving boundary problem under study is firstly transformed in a fixed boundary one, allowing the computation of the propagation front as a new unknown that can be computed together with the mass concentrations of CO 2 in air and water. Apart from the stability and the consistency of the numerical solution, constructed by a finite difference scheme, qualitative properties of the numerical solution are established. In fact, positivity of the concentrations, increasing properties of the propagation front and monotone behavior of the solution are proved. We also confirm numerically the √ t-law of propagation. Results are illustrated with numerical examples.

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“…Numerical simulations of the solution of carbonation problems using the finite element method have been performed in [14,15].…”

Section: Introductionmentioning

confidence: 99%

Computing positive stable numerical solutions of moving boundary problems for concrete carbonation

Piqueras

Jódar

2018

Journal of Computational and Applied Mathematics

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“…In fact, in the next example, according to data from [13], we match the numerical solution of the carbonation front as a function of the type C√t.…”

Section: Numerical Evidences Of the √T-law Of Propagationmentioning

confidence: 99%

“…Furthermore, they also justify rigorously that the carbonation front S (t) satisfies a long time behaviour of the type C 1 √t ≤ S(t) ≤ C 2 √t, when the exposed boundary conditions are constant, G(t) = G*, H(t) = H*, and linked by the condition G* = γH*. Numerical simulations of the solution of carbonation problems using the finite element method have been performed in [12,13].…”

Section: Introductionmentioning

confidence: 99%

Solving Moving Boundary Concrete Carbonation Models

Piqueras¹,

Company²,

Jódar³

2017

dtcse

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Abstract. In this work we present a finite difference method to solve a coupled mixed partial differential equation system arising in concrete carbonation problems. The free boundary problem under study is firstly transformed in a fixed boundary one, allowing the computation of the propagation front as a new unknown that can be computed together with the mass concentrations of CO2 in air and water. Apart from the stability and the consistency of the numerical solution, constructed by a finite difference scheme, qualitative properties of the numerical solution are established without proof. In fact, positivity of the concentrations, increasing properties of the propagation front and monotone behaviour of the solution are proved. We also confirm numerically the √t-law of propagation.

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“…The classic problem with moving boundary is the Stefan problem. Other examples can be the following problems: solidification-meltdown [19], wound healing [20], concrete carbonation [21,22], issues concerning processes of evaporation, condensation [17,23]. There are not general solution techniques for problems with unknown moving boundaries, and virtually any of such nonlinear problems requires developing special approaches.…”

Section: Introductionmentioning

confidence: 99%

Mathematical model on surface reaction diffusion in the presence of front chemical reaction

Permikin

Zverev

2013

International Journal of Heat and Mass Transfer

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a b s t r a c tThe article discusses a mathematical model of solid-phase diffusion over substance surface accompanied a frontal chemical reaction. The purpose of our article is to describe the concentration distribution and surface reacted layer growth. The model is a system parabolic equations, complicated with the presence of mobile front. It takes account of diffusive fluxes redistribution, sublimation from the surface, chemical reaction reversibility. The asymptotic approximation of the obtained nonlinear problem is constructed. Numerical solution was also carried out. Both numerical and analytical solutions conform to each other in a wide range of parameter changes, whereas observed differences are explained. It was obtained that the reaction front at the substrate surface grows as the fourth root of time in the assumed absence of evaporation and reaction reversibility. In the presence of evaporation the logarithmic distribution law ln(t) is obtained. The theoretical possibility of sharp deceleration and stop of reaction product layer growth is obtained.

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Moving carbonation fronts in concrete: A moving-sharp-interface approach

Cited by 42 publications

References 24 publications

Computing positive stable numerical solutions of moving boundary problems for concrete carbonation

Computing positive stable numerical solutions of moving boundary problems for concrete carbonation

Solving Moving Boundary Concrete Carbonation Models

Mathematical model on surface reaction diffusion in the presence of front chemical reaction

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