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Abstract and Figures

Comparisons of experimental observation of heat and moisture transfer through porous building materials with numerical results have been presented in numerous studies reported in the literature. However, some discrepancies have been observed, highlighting underestimation of sorption process and overestimation of desorption process. Some studies intend to explain the discrepancies by analysing the importance of hysteresis effects as well as carrying out the sensitivity analysis on the input parameters as convective transfer coefficients. This article intends to investigate the accuracy and efficiency of the coupled solution by adding advective transfer of both heat and moisture in the physical model. The efficient Scharfetter-Gummel numerical scheme is proposed to solve the system of advection-diffusion equations, which has the advantages of being well-balanced and asymptotically preserving. Moreover, the scheme is particularly efficient in terms of accuracy and reduction of computational time when using large spatial discretization parameters. Several linear and nonlinear cases are studied to validate the method and highlight its specific features. At the end, an experimental benchmark from the literature is considered. The numerical results are compared with the experimental data for a purely diffusive model and also for the proposed model. The latter presents better agreement with the experimental data. The influence of the hysteresis effects on the moisture capacity is also studied, by adding a third differential equation.
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Transp Porous Med (2018) 121:665–702
https://doi.org/10.1007/s11242-017-0980-3
On the Solution of Coupled Heat and Moisture Transport
in Porous Material
Julien Berger1·Suelen Gasparin2,3·
Denys Dutykh3·Nathan Mendes2
Received: 10 July 2017 / Accepted: 28 November 2017 / Published online: 13 December 2017
© Springer Science+Business Media B.V., part of Springer Nature 2017
Abstract Comparisons of experimental observation of heat and moisture transfer through
porous building materials with numerical results have been presented in numerous studies
reported in the literature. However, some discrepancies have been observed, highlighting
underestimation of sorption process and overestimation of desorption process. Some studies
intend to explain the discrepancies by analyzing the importance of hysteresis effects as well
as carrying out sensitivity analyses on the input parameters as convective transfer coefficients.
This article intends to investigate the accuracyand efficiency of the coupled solution by adding
advective transfer of both heat and moisture in the physical model. In addition, the efficient
Scharfetter and Gummel numerical scheme is proposed to solve the system of advection–
diffusion equations, which has the advantages of being well-balanced and asymptotically
preserving. Moreover, the scheme is particularly efficient in terms of accuracy and reduction
of computational time when using large spatial discretization parameters. Several linear and
nonlinear cases are studied to validate the method and highlight its specific features. At the
end, an experimental benchmark from the literature is considered. The numerical results
are compared to the experimental data for a pure diffusive model and also for the proposed
model. The latter presents better agreement with the experimental data. The influence of
the hysteresis effects on the moisture capacity is also studied, by adding a third differential
equation.
Electronic supplementary material The online version of this article (https://doi.org/10.1007/s11242-
017-0980- 3) contains supplementary material, which is available to authorized users.
BJulien Berger
julien.berger@univ-smb.fr
1LOCIE, UMR 5271, CNRS, Université Savoie Mont Blanc, 73000 Chambéry, France
2Thermal Systems Laboratory, Mechanical Engineering Graduate Program, Pontifical Catholic
University of Paraná, Rua Imaculada Conceição, 1155, Curitiba, Paraná CEP 80215-901, Brazil
3LAMA, UMR 5127 CNRS, Université Savoie Mont Blanc, Campus Scientifique, 73376
Le Bourget-du-Lac Cedex, France
123
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... The Scharfetter-Gummel numerical scheme was proposed in 1969 in [36] with very recent theoretical results in [18,19]. In the context of building porous media, it is successfully applied in [5] to water transport and then in [6] to combined heat and moisture transfer. The contributions of the present paper is two fold. ...
... It has been shown that the diffusion of moisture can be written using the vapor pressure P 1 , introducing the global moisture permeability k m [6]. Thus, the total moisture flux yields: ...
... The moisture and heat equations are advection-diffusion types. The Scharfetter-Gummel approach has shown great efficiency in preliminary studies for a single equation [5] and a system of two coupled equations [6]. Therefore it will be used for the spatial discretisation of the moisture and heat equations. ...
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This work presents a detailed mathematical model combined with an innovative efficient numerical model to predict heat, air and moisture transfer through porous building materials. The model considers the transient effects of air transport and its impact on the heat and moisture transfer. The achievement of the mathematical model is detailed in the continuity of Luikov's work. A system composed of two advection-diffusion differential equations plus one exclusively diffusion equation is derived. The main issue to take into account the transient air transfer arises in the very small characteristic time of the transfer, implying very fine discretisation. To circumvent these difficulties, the numerical model is based on the Du Fort-Frankel explicit and unconditionally stable scheme for the exclusively diffusion equation. It is combined with a two-step Runge-Kutta scheme in time with the Scharfetter-Gummel numerical scheme in space for the coupled advection-diffusion equations. At the end, the numerical model enables to relax the stability condition, and, therefore, to save important computational efforts. A validation case is considered to evaluate the efficiency of the model for a nonlinear problem. Results highlight a very accurate solution computed about 16 times faster than standard approaches. After this numerical validation, the reliability of the mathematical model is evaluated by comparing the numerical predictions to experimental observations. The latter is measured within a multi-layered wall submitted to a sudden increase of vapor pressure on the inner side and driven climate boundary conditions on the outer side. A very satisfactory agreement is noted between the numerical predictions and experimental observations indicating an overall good reliability of the proposed model.
... In February 2019 this journal published the article "An efficient numerical model for liquid water uptake in porous material and its parameter estimation" [1], which reintroduces the Scharfetter-Gummel numerical model for simulation of moisture transfer in building materials, and applies it for the inverse characterisation of hygric properties based on a capillary absorption experiment. Given that this research group has liberally published on Scharfetter-Gummel for hygrothermal simulation [2][3][4][5] as well as on inverse characterisation for hygrothermal properties [6][7][8][9] already, the single novelty of [1] is its focus on capillary absorption. This critique however voices serious concerns on the validity of the moisture transfer model defined, of the moisture transfer simulations performed, and of the moisture transfer properties identified. ...
... Given that this research group has liberally published on Scharfetter-Gummel for hygrothermal simulation [2][3][4][5] as well as on inverse characterisation for hygrothermal properties [6][7][8][9] already, the single novelty of [1] is its focus on capillary absorption. With respect to that, [1] claims that a simple capillary absorption experiment -wherein only the height of the moisture front is monitored -suffices for a complete characterisation of the moisture storage and transport properties of the material. ...
... The sections above have formulated several serious concerns on the dependability of the moisture transfer model defined, of the moisture transfer simulations performed, and of the moisture transfer properties identified in [1]. Introductorily, this research group has liberally published on the Scharfetter-Gummel method for hygrothermal simulation [1][2][3][4][5], and in all of these publications the efficiency of the scheme is touted. The discusser's Delphin simulations expose the unfounded nature of such claim though, as these are about 50 times faster than [1]'s simulations. ...
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... Then, for the heat and mass advection-diffusion Equations (2a) and (2b), the SCHARFETTER-GUMMEL numerical scheme is used. Preliminary studies 23,24 showed the efficiency of the approach to extend the stability conditions and the accuracy of the solution. As a last step of the proposed methodology, the time discretisation of these two equations, an innovative two-step RUNGE-KUTTA approach is used of the time discretisation of these two advection-diffusion equations, enabling to extend further the stability region of the numerical scheme. ...
... = (1) and we obtain Δt ≤ CΔx. 24 Thus, it is one order less restrictive than standard approach and the so-called COURANT-FRIEDRICHS-LEWY (CFL) conditions Δt ≤ CΔx 2 . Using, the SCHARFETTER-GUMMEL scheme, the spatial discretisation does not need to be extremely refined. ...
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... This can be explained by the fact that advection of vapor due to gas transport is almost always neglected. But this quite common simplification has not got any consensus, since some authors have already underlined that air flows may have a significant impact on the hygroscopic behavior of porous material like concrete [20], textiles [21], or even earthen and bio-based materials [22]. ...
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... As discussed and thoroughly motivated in [15][16][17], it is of capital importance to obtain a dimensionless problem before elaborating a numerical model. For this, dimensionless fields are defined: ...
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Chapter
Numerical methods for the solution of initial value problems in ordinary differential equations made enormous progress during the 20th century for several reasons. The first reasons lie in the impetus that was given to the subject in the concluding years of the previous century by the seminal papers of Bashforth and Adams for linear multistep methods and Runge for Runge–Kutta methods. Other reasons, which of course apply to numerical analysis in general, are in the invention of electronic computers half way through the century and the needs in mathematical modelling of efficient numerical algorithms as an alternative to classical methods of applied mathematics. This survey paper follows many of the main strands in the developments of these methods, both for general problems, stiff systems, and for many of the special problem types that have been gaining in significance as the century draws to an end. © 2000 Elsevier Science B.V. All rights reserved.
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