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Current hygrothermal behaviour prediction models neglect the hysteresis phenomenon. This leads to a discrepancy between numerical and experimental results, and a miscalculation of buildings' durability. In this paper, a new mathematical model of hysteresis is proposed and implemented in a hygrothermal model to reduce this discrepancy. The model is based on a symmetry property between sorption curves and uses also a homotopic transformation relative to a parameter s ∈ [ 0 , 1 ]. The advantage of this model lies in its ease of use and implementation since it could be applied with the knowledge of only one main sorption curve by considering s = 0 , in other words, we only use the axisymmetric property here. In the case where the other main sorption curve is known, we use this curve to incorporate the homotopy property in order to calibrate the parameter s.The full version of the proposed model is called Axisymmetric + Homotopic. Furthermore, it was compared not only with the experimental sorption curves of different types of materials but also with a model that is well known in the literature (CARMELIET's model). This comparison shows that the Axisymmetric + Homotopic model reliably predicts hysteresis loops of various types of materials even with the knowledge of only one of the main sorption curves. However, the full version of Axisymmetric + Homotopic model is more reliable and covers a large range of materials. The proposed model was incorporated into the mass transfer model. The simulation results strongly match the experimental ones. [ABSTRACT FROM AUTHOR]

The design of numerical tools to model the behavior of building materials is a challenging task. The crucial point is to save computational costs and maintain the high accuracy of predictions. There are two main limitations on the time scale choice, which places an obstacle to solving the above issues. The first one is the numerical restriction. A number of research studies are dedicated to overcome this limitation and it is shown that it can be relaxed with innovative numerical schemes. The second one is the physical restriction. It is imposed by the properties of a material, the phenomena itself, and the corresponding boundary conditions. This study is focused on the study of a methodology that enables to overcome the physical restriction on the time grid; a so‐called average reduced model is suggested. It is based on smoothing the time‐dependent boundary conditions. Besides this, the approximate solution is decomposed into average and fluctuating components. The primer is obtained by integrating the equations over time, whereas the latter is a user‐defined EM. The methodology is investigated for both heat diffusion and coupled heat and mass transfer. It is demonstrated that the signal core of the boundary conditions is preserved and the physical restriction can be relaxed. The model proved to be reliable, accurate, and efficient also in comparison with the experimental data of 2 years. The implementation of the scarce time‐step of 1h is justified. It is shown, that by maintaining the tolerable error, it is possible to cut computational effort up to almost four times in comparison with the complete model with the same time grid. [ABSTRACT FROM AUTHOR]

Highlights • A detailed mathematical model for the heat, air and mass transfer is achieved. • An efficient numerical model is proposed to save computational efforts. • Demonstration of numerical model efficiency (cpu time, accuracy) for a case study. • Evaluation of the reliability of the model by confronting to experimental results. Abstract 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 L uikov '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 D u F ort –F rankel explicit and unconditionally stable scheme for the exclusively diffusion equation. It is combined with a two–step R unge –K utta scheme in time with the S charfetter –G ummel 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. [ABSTRACT FROM AUTHOR]

This paper proposes a reduced order model to simulate heat and moisture behaviour of material based on proper general decomposition (PGD). This innovative method is ana priorimodel reduction method. It proposes an alternative way for computing solutions of the problem by considering a separated representation of the solution. PGD offers an interesting reduction of numerical cost. In this paper, the PGD solution is first compared with a finite element solution and the commercial validated modelDelphinin an 1D case. The results show that the PGD resolution techniques enable the field of interest to be represented with accuracy, with a relative error rate of less than 0.1%. The study remains in the hygroscopic range of the material. As the numerical gain of the method becomes interesting when the space dimension increases, this resolution strategy was then used on a 2D multi-layered test case. The dynamics and amplitude of hygrothermal fields are perfectly represented by the PGD solution. Temperature and vapour pressure modelled with PGD can be used for post-processing and analysing the behaviour of an assembly. [ABSTRACT FROM PUBLISHER]

The reliability of mathematical models for heat and mass transfer in building porous material is of capital importance. A reliable model permits to carry predictions of the physical phenomenon with sufficient confidence in the results. Among the physical phenomena, the hysteresis effects on moisture sorption and moisture capacity need to be integrated in the mathematical model of transfer. This article proposes to explore the use of an smooth Bang–Bang model to simulate the hysteresis effects coupled with heat and mass transfer in porous material. This model adds two supplementary differential equations to the two classical ones for heat and mass transfer. The solution of these equations ensures smooth transitions between the main sorption and desorption curves. Two parameters are required to control the speed of transition through the intermediary curves. After the mathematical description of the model, an efficient numerical model is proposed to compute the fields with accuracy and reduced computational efforts. It is based on the Du Fort–Frankel scheme for the heat and mass balance equations. For the hysteresis numerical model, an innovative implicit–explicit approach is proposed. Then, the predictions of the numerical model are compared with experimental observations from literature for two case studies. The first one corresponds to a slow cycle of adsorption and desorption while the second is based on a fast cycling case with alternative increase and decrease of moisture content. The comparisons highlight a very satisfactory agreement between the numerical predictions and the observations. In the last Section, the reliability and efficiency of the proposed model is investigated for long term simulation cases. The importance of considering hysteresis effects in the reliability of the predictions are enhanced by comparison with classical approaches from literature. • Building numerical model for heat and mass transfer with hysteresis effects. • Use of Bang–Bang model for modeling hysteresis on moisture sorption and capacity. • Comparison of the model reliability with two experimental benchmark from literature. • Saved computational effort and satisfactory agreement with experimental observations. [ABSTRACT FROM AUTHOR]

• Reliability of model for heat and mass transfer in porous material is achieved. • An efficient numerical model is proposed to save computational efforts. • Inverse problem is solved to estimate uncertain input parameter. • Identifiability of the seven unknown coefficients is demonstrated. • Other experimental data are used to benchmark the numerical prediction of the model. The reliability of a model is its accuracy in predicting the physical phenomena. In this paper, the robustness of a model of heat and mass transfer in a porous material is evaluated by comparing the numerical predictions with experimental observations. An experimental facility composed of an enclosure made with spruce CLT panels is used. An increase of temperature is applied in the inside air volume to force the heat transfer from the inner to the outer surfaces. Sensors inside the material enables to have experimental observations of the physical phenomena. Before bench-marking the numerical model, a first set of experimental data is used to reduce the two major source of uncertainties in the model. Indeed, the first source arises from surface heat and mass transfer coefficients, usually determined by empirical correlations. The second comes the thermal conductivity of the material which is defined through standard methods as invariant for the three layers of the spruce panels. To overcome this issue, a set of seven uncertain parameters are estimated using an hybrid optimizer after demonstrating their theoretical and practical identifiability. Then, the reliability of the numerical model, based on the Du Fort–Frankel explicit scheme, is evaluated by comparison to a second set of experimental data obtained in another wall of the enclosure. A very satisfactory agreement is remarked showing the accuracy of the model to predict the physical phenomena in this hygroscopic porous material. [ABSTRACT FROM AUTHOR]