A class of coupled nonlinear reaction diffusion models exhibiting fingering

Carey, G. F.; Fowkes, Neville; Staelens, A.; Pardhanani, Anand L.

doi:10.1016/j.cam.2003.09.037

Cited by 6 publications

(5 citation statements)

References 3 publications

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“…The transport of CO2 in concrete gaseous phase can be described by using Fick laws with considering the consumption of CO2 due to carbonation as follows [25,26,27],…”

Section: Modelling Of Carbon-dioxide Diffusion In Concrete With General Carbonation Reactionmentioning

confidence: 99%

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Mathematical modelling of concrete carbonation with moving boundary

Li¹,

Li²,

Wang³

2020

International Communications in Heat and Mass Transfer

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This paper presents the mathematical models describing the diffusion of carbon-dioxide in concrete with considering the effect of concrete carbonation. The effect of concrete carbonation on carbon-dioxide diffusion is modelled by using a sink term added in the diffusion equation.It is shown that, when the carbonation reaction is much faster than the diffusion process, the diffusion of carbon-dioxide in carbonated concrete can be treated as the diffusion problem with a moving boundary, representing the diffusion front or the carbonation depth. An analytical solution is also derived for the diffusion problem with moving boundary.

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“…The transport of CO2 in concrete gaseous phase can be described by using Fick laws with considering the consumption of CO2 due to carbonation as follows [25,26,27],…”

Section: Modelling Of Carbon-dioxide Diffusion In Concrete With General Carbonation Reactionmentioning

confidence: 99%

“…Eqs. ( 6)-( 11) can be solved using numerical methods such as the finite difference method [26,27]. Fig.…”

Section: Modelling Of Carbon-dioxide Diffusion In Concrete With General Carbonation Reactionmentioning

confidence: 99%

Mathematical modelling of concrete carbonation with moving boundary

Li¹,

Li²,

Wang³

2020

International Communications in Heat and Mass Transfer

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“…The elements of the matrices H, P and Q can be evaluated according to (2) and (3). H mXm D h m ðt 0 Þ h m ðt 1 Þ À À À À À Àh m ðt mÀ1 Þ ½ ; ð3Þ…”

Section: Haar Wavelet Preliminariesunclassified

Review of wavelet methods for the solution of reaction–diffusion problems in science and engineering

Hariharan

Kannan

2014

Applied Mathematical Modelling

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a b s t r a c tWavelet method is a recently developed tool in applied mathematics. Investigation of various wavelet methods, for its capability of analyzing various dynamic phenomena through waves gained more and more attention in engineering research. Starting from 'offering good solution to differential equations' to capturing the nonlinearity in the data distribution, wavelets are used as appropriate tools at various places to provide good mathematical model for scientific phenomena, which are usually modeled through linear or nonlinear differential equations. Review shows that the wavelet method is efficient and powerful in solving wide class of linear and nonlinear reaction-diffusion equations. This review intends to provide the great utility of wavelets to science and engineering problems which owes its origin to 1919. Also, future scope and directions involved in developing wavelet algorithm for solving reaction-diffusion equations are addressed.Crown

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“…These models, in general, employ an association between the factors that influence the alkaliaggregate reaction in order to determine the expansion ratio. Also employing Arrhenius law, Carey et al [9] modeled the gel concentration and diffusion in order to obtain its distribution in a structure, leading to coupled equations which are numerically solved employing the finite element method. Among those, there are other expansion models that employ the factors that affect the AAR for evaluating the expansion [10,11].…”

Section: Introductionmentioning

confidence: 99%

Numerical Modeling of Orthotropic Concrete Expansion Due to Alkali-Aggregate Reaction With a Parametric Model

Carrazedo¹,

Sanches²,

Lacerda³

2014

Proceedings of 10th World Congress on Computational Mechanics

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The alkali-aggregate reaction (AAR) in concrete structures consists in a chemical deleterious reaction between alkalis liberated during hydration of cement and reactive minerals present on aggregates. The process leads to the formation of a gel, which in presence of hydroxyl ions expands, causing cracks in concrete, promoting its volume variation, followed by reduction of important properties, such as the Young´s modulus and mechanical strength. Modeling of a structure subjected to AAR expansion may predict the structural displacements and strains due to the reaction, enabling programming efficient structural maintenance operations , reducing temporary interruptions and also increasing safety conditions. As such, this work presents a parametric model for simulating the orthotropic concrete expansion due to alkali-aggregate reaction, based on Carrazedo and Lacerda, 2008 [1].

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A class of coupled nonlinear reaction diffusion models exhibiting fingering

Cited by 6 publications

References 3 publications

Mathematical modelling of concrete carbonation with moving boundary

Mathematical modelling of concrete carbonation with moving boundary

Review of wavelet methods for the solution of reaction–diffusion problems in science and engineering

Numerical Modeling of Orthotropic Concrete Expansion Due to Alkali-Aggregate Reaction With a Parametric Model

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