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This work presents an alternative view on the numerical simulation of diffusion processes applied to the heat and moisture transfer through multilayered porous building materials. Traditionally, by using the finite-difference approach, the discretization follows the Method Of Lines (MOL), when the problem is first discretized in space to obtain a large system of coupled Ordinary Differential Equations (ODEs). This paper proposes to change this
viewpoint. First, we discretize in time to obtain a small system of coupled ODEs, which means instead of having a Cauchy (Initial Value) Problem (IVP), we have a Boundary Value Problem (BVP). Fortunately, BVPs can be solved efficiently today using adaptive collocation finite-difference methods of high order. To demonstrate the benefits of this new approach, three case studies are presented. The first one considers nonlinear heat and moisture transfer through one material layer. The second case includes the rain effect, while the last one considers two material layers. Results show how the nonlinearities and the interface between materials are easily treated, by reasonably using a fourth-order adaptative method. In our numerical simulations, we use adaptive methods of the fourth order which in most practical situations is more than enough.

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... An absolute error ε 2 of 5.21 Pa and 0.29 • C and a relative error error ε 2,,r of 0.08 and 0.04 are obtained between the experimental data and the interpolated initial profiles of vapor pressure and temperature, respectively. Some complementary information on the experimental design is given in [14]. ...

... If the reliability of the proposed model is very satisfactory, most approaches from the literature do not consider the air transport equation (2.14c). For instance, in [14] the reliability is proven for the same case study but considering a model with only heat and moisture transport by diffusion processes. A natural question raises on the importance of considering air transport to better represent the whole physical phenomenon. ...

... A natural question raises on the importance of considering air transport to better represent the whole physical phenomenon. To answer this question, the numerical predictions from the model in [14], denoted as HM (Heat and Moisture) model are compared to the one obtained with the proposed model, denoted as HAM (Heat, Air and Moisture) model. Figure 12 shows the probability density function of the relative error for each model between the numerical predictions and the experimental observations. ...

... An absolute error ε 2 of 5.21 Pa and 0.29 • C and a relative error error ε 2,,r of 0.08 and 0.04 are obtained between the experimental data and the interpolated initial profiles of vapor pressure and temperature, respectively. Some complementary information on the experimental design is given in [14]. ...

... If the reliability of the proposed model is very satisfactory, most approaches from the literature do not consider the air transport equation (2.14c). For instance, in [14] the reliability is proven for the same case study but considering a model with only heat and moisture transport by diffusion processes. A natural question raises on the importance of considering air transport to better represent the whole physical phenomenon. ...

... A natural question raises on the importance of considering air transport to better represent the whole physical phenomenon. To answer this question, the numerical predictions from the model in [14], denoted as HM (Heat and Moisture) model are compared to the one obtained with the proposed model, denoted as HAM (Heat, Air and Moisture) model. Figure 12 shows the probability density function of the relative error for each model between the numerical predictions and the experimental observations. ...

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.

... Then, a boundary value problem is defined to compute the spatial coefficients of the reduced model. The idea originates from recent works on the method of horizontal lines proposed in [34]. Then, a step further is proposed compared to approaches from the literature in building physics. ...

... Another method is explored following the works on horizontal lines applied to complete models in [34,51]. The proposed approximation of the solution is the following: ...

Within the environmental context, numerical modeling is a promising approach to assess the energy efficiency of building. Resilient buildings need to be designed, capable of adapting to future extreme heat. Simulations are required assuming a one-dimensional heat transfer problem through walls and a simulation horizon of several years (nearly 30). The computational cost associated with such modeling is quite significant and model reduction methods are worth investigating. The objective is to propose a reliable reduced-order model for such long-term simulations. For this, an alternative model reduction approach is investigated, assuming a known Proper Orthogonal Decomposition reduced basis for time, and not for space as usually. The model enables computing parametric solutions using basis interpolation on the tangent space of the Grassmann manifold. Three study cases are considered to verify the efficiency of the reduced-order model. Results highlight that the model has a satisfying accuracy of 10-3 compared to reference solutions. The last case study focuses on the wall energy efficiency design under climate change according to a four-dimensional parameter space. The latter is composed of the load material emissivity, heat capacity, thermal conductivity and thickness insulation layer. Simulations are carried over 30 years considering climate change. The solution minimizing the wall work rate is determined with a computational ratio of 0.1% compared to standard approaches.

... Its estimation would be based on the solution of coupled heat and mass transfer equations [46,47,48]. The initial condition is the one reached by the material after the preconditioning phase. ...

Similarities are mathematical laws, which are based on the dimensionless formulation of the governing equation of a physical phenomenon. Consequently, a set of characteristic dimensionless numbers is obtained. Similarities aim, via these numbers, to find equivalences between particular configurations. This approach is widely adopted, especially in fluid and aerodynamic problems. In the building context, the phenomena of heat and mass transfer in porous media occur with slow kinetics. Thus, similarities can be employed to reduce the duration of experimental campaigns to characterize material properties. These laws were investigated here in the case of a heat transfer problem through an experimental campaign. Two equivalent configurations were submitted to a heat stress. Temperatures inside materials were measured and compared to assess the validity of thermal similarity. A complete evaluation of uncertainty propagation was then carried out. Uncertainties related to the sensor position, its response time, the omission of mass transfer, the sensor systematic accuracy, the random measurement aspect, the one-dimensional transfer hypothesis and the boundary condition modeling were evaluated. The comparison of both configurations was carried out based on the confidence interval of both measurements. The results showed a good agreement between the reference and reduced experiment. On the basis of these findings, similarities were experimentally verified within a margin of discrepancy that was justified. Thus, they can be adopted in heat transfer experiments in order to identify equivalent configurations that are easier to conduct.

... They used WUFI software to solve the non-linear transport equations. Over the past twenty years, many mathematical models and numerical methods applying to different fields have been described [5][6][7][8][9][10][11]. ...

Plant-based concrete is a construction material which, in addition to having a very low environmental impact, exhibits excellent hygrothermal comfort properties. It is a material which is, as yet, relatively unknown to engineers in the field. Therefore, an important step is to implement reliable mass-transfer simulation methods. This will make the material easy to model, and facilitate project design to deliver suitable climatic conditions. In recent decades, numerous studies have been carried out to develop models of the coupled transfers of heat, air and moisture in porous building envelopes. Most previous models are based on Luikov’s theory, considering mass accumulation, air and total pressure gradient. This theory considers the porous medium to be homogeneous, and therefore allows for hygrothermal transfer equations on the basis of the fundamental principles of thermodynamics. This study presents a methodology for solving the classical 1D (one-dimensional) HAM (heat, air, and moisture) hygrothermal transfer model with an implementation in MATLAB. The resolution uses a discretization of the problem according to the finite-element method. The detailed solution has been tested on a plant-based concrete. The energy and mass balances are expressed using measurable transfer quantities (temperature, water content, vapor pressure, etc.) and coefficients expressly related to the macroscopic properties of the plant-based concrete (thermal conductivity, specific heat, water vapor permeability, etc.), determined experimentally. To ensure this approach is effective, the methodology is validated on a test case. The results show that the methodology is robust in handling a rationalization of the model whose parameters are not ranked and not studied by their degree of importance.

... In this context, the initial boundary value problem Eq. (5) is semi-discretized along the time line [9]. The time discretization parameter is denoted by ∆t , corresponding to the time step of coupling between the numerical models of the co-simulation. ...

Estimating the temperature field of a building envelope could be a time-consuming task. The use of a reduced-order method is then proposed: the Proper Generalized Decomposition method. The solution of the transient heat equation is then re-written as a function of its parameters: the boundary conditions, the initial condition, etc. To avoid a tremendous number of parameters, the initial condition is parameterized. This is usually done by using the Proper Orthogonal Decomposition method to provide an optimal basis. Building this basis requires data and a learning strategy. As an alternative, the use of orthogonal polynomials (Chebyshev, Legendre) is here proposed.

... For the sake of clarity, the so-called global heat storage coefficient c T W · s/(m 3 · K) is introduced as in [36]: ...

... The moisture transfer is driven by vapor and liquid diffusions. According to [12,23], the mathematical model to represent the energy and mass conservation in a building porous material can be formulated as follows: ...

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 DuFort-Frankel scheme for the heat and mass balance equations. For the hysteresis numerical model, an innovative implici-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.

In order to better predict the hygrothermal behavior of porous building envelopes, it is essential to develop reliable mathematical models which accurately capture the coupled heat, air, and mass (HAM) transport and its influence on the indoor atmosphere. Recently, numerous models have been developed to predict the performance of bio-based building envelopes. However, the large number of input parameters and lack of knowledge of the intrinsic characteristics of the materials mean these models are quite difficult to implement. To determine the most influential hygrothermal parameters for a hemp concrete wall, a sensitivity study was conducted on the input parameters, based on the probability density distribution of Gaussian centered law; the results are presented herein. A reduced model was developed by eliminating the parameters with little or no influence on HAM transfer. Then, a dimensionless study of the reduced model was carried out. This generated an indicative parameter ς, which can be used to classify building materials and identify the most suitable. In MATLAB software, the simulated results for a hemp concrete wall showed satisfactory concordance with the experimental results found in the literature. The temperature profiles are accurately estimated. Note that the model must always take account of the evolution of water content to ensure accurate RH predictions.

Realizing dynamic thermal comfort can help improve building performance. The heat and moisture transfer of the envelope is an important part of building performance. Therefore, this paper takes a typical room in Shanghai as an example and uses simulation software WUFI-PLUS and DELPHIN to study the influence of dynamic/steady-state operation mode of indoor air conditioning on the heat and moisture transfer of the envelope structure. The results show that based on the same thermal comfort, the energy consumption of the full heat load in dynamic operation mode is 73.69% lower than that in steady-state operation mode at 0ACH night ventilation, and it is 65.10% lower at 5ACH night ventilation. And at the same night ventilation condition, the moisture flow through the wall in the dynamic operating mode is smaller than that in the steady-state operating mode. In the case of 0ACH, when the partial pressure difference of water vapor is positive, the moisture transfer capacity in the dynamic operation mode of the indoor thermal environment is 11.7% lower than that in the steady-state operation mode. Therefore, when the partial pressure difference of water vapor is positive, the dynamic change of the indoor thermal environment can reduce the latent heat load of the envelope under the same water vapor pressure difference.

Estimating the temperature field of a building envelope could be a time-consuming task. The use of a reduced-order method is then proposed: the Proper Generalized Decomposition method. The solution of the transient heat equation is then re-written as a function of its parameters: the boundary conditions, the initial condition, etc. To avoid a tremendous number of parameters, the initial condition is parameterized. This is usually done by using the Proper Orthogonal Decomposition method to provide an optimal basis. Building this basis requires data and a learning strategy. As an alternative, the use of orthogonal polynomials (Chebyshev, Legendre) is here proposed.
Highlights
• Chebyshev and Legendre polynomials are used to approximate the initial condition
• Performance of Chebyshev and Legendre polynomials are compared to the POD basis
• Each basis combined with the PGD model is compared to laboratory measurements
• The influence of four different parameters on the accuracy of the basis is studied
• For each approximation basis, CPU calculation times are evaluated and compared

Building energy consumption is directly impacted by weather parameters such as temperature, solar radiation, atmospheric pressure, relative humidity and wind velocity. The knowledge of the building hygrothermal performance enables the design of energy efficient buildings and the prediction of overall durability and sustainability of envelopes. Therefore, designers and builders are interested in modeling the long-term performance of the envelopes by means of accurate, reliable and fast simulation tools.Several numerical models have been proposed in the literature to study the heat and moisture transfer in building materials. In general, this problem is solved by traditional methods, such as finite-difference and finite-volume methods, using mainly implicit schemes. Nevertheless, these methods impose costly sub-iterations to treat the nonlinearities and very fine discretization, which increase substantially the simulation computational cost. Therefore, this research has been focused on the development and analyses of numerical methods for efficiently simulate the problem of heat and mass transfer through porous materials.In the first part of this thesis, improved schemes of the traditional numerical methods have been developed to eliminate costly sub-iterations to treat nonlinearities, to improve the order of accuracy and to save computer run time. Despite the great progress with the new numerical schemes, the conclusion of the first part shows that we still have to deal with large systems of equations, particularly when treating multi-dimensional transfer problems. For this reason, to reduce even more the computational burden and the size of the system, a reduced-order model, based on spectral methods is proposed in the sequence to provide an accurate description of the physical phenomena. The degrees of freedom of the solution is strongly decreased while maintaining the model fidelity. It ensures a computational cost much lower than the complete original model.All these methods are applied to problems related to building physics, such as single and multilayer nonlinear transfer, the determination of optimum insulation thickness, the process of moisture buffer effects and transfer in one- or two-zone building models. In conclusion, we show how to build efficient numerical models, in terms of computational cost and accuracy, to investigate the heat and mass transfer in porous materials.

A precise hygrothermal model is essential to predict the energy performance of building envelopes providing coupled transport of mass (moisture and air) and heat through porous elements, considering phase change and all heat transfer modes, including the radiative transfer through fibrous materials. Therefore, a new mathematical model, called CAR-HAM (Conductive, Advective, and Radiative Heat, Air and Moisture), is proposed to include the radiative transfer equation to calculate the thermal radiation effects within the porous materials to be taken into account in the energy balance. The moisture and the energy conservation equations are simultaneously solved using a fully implicit scheme and the MTDMA algorithm. The comparison of the proposed model considering some case studies such as attic insulation, bar drying, convection and high humidity (rain load) - showed a good agreement with experimental data available in the literature.

Much disparity exists on the numerical efficiency and accuracy of different potentials for moisture transfer in building materials, with various implicit claims but no actual corroboration. This paper aims at providing such evidence by comparing the numerical efficiency and accuracy of capillary pressure, relative humidity and -log(-capillary pressure) for a suite of benchmark simulations. The study shows that capillary pressure and relative humidity outperform -log(-capillary pressure), as the latter is plagued by its highly non-linear moisture capacity near saturation. Capillary pressure and relative humidity are thus the potentials of choice.

This paper proposes the application of the covariance matrix adaptation (CMA) evolution strategy for the identification of building envelope materials hygrothermal properties. All material properties are estimated on the basis of local temperature and relative humidity measurements, by solving the inverse heat and moisture transfer problem. The applicability of the identification procedure is demonstrated in two stages: first, a numerical benchmark is developed and used as to show the potential identification accuracy, justify the choice for a Tikhonov regularization term in the fitness evaluation, and propose a method for its appropriate tuning. Then, the procedure is applied on the basis of experimental measurements from an instrumented test cell, and compared to the experimental characterization of the observed material. Results show that an accurate estimation of all hygrothermal properties of a building material is feasible, if the objective function of the inverse problem is carefully defined.

Simulation models for moisture transfer in building materials are highly incongruent with respect to the moisture potential used. Often the relatively better numerical efficiency and accuracy of a certain moisture potential is put forward as motivation. Various claims are made in that respect, but factual evidence is typically lacking. This paper aims at providing such support by assessing simulation efficiency and accuracy for capillary pressure, relative humidity and -log(-capillary pressure). To that goal, a suite of benchmark simulations are performed with those three potentials and performances are compared, based on deviations from reference solutions and on numbers of iterations required. The study initially reveals mixed results, showing no consistent advantages for either potential. Further analysis uncovers though that -log(-capillary pressure) suffers from a strongly nonlinear moisture capacity near saturation. This finally results in a decision in favour of capillary pressure and relative humidity, at least for general-purpose moisture transfer simulation.

This paper presents an experimental and quantitative analysis of capillary transport across the interface brick–mortar joint in masonry. Moisture profiles are measured with X-ray projection. The influence of curing conditions is analyzed by considering three types of mortars: cured in a mould, between capillary wet and dry bricks. A decrease in moisture inflow for the mortars cured between bricks is measured. The pore structure and the moisture transport properties of mortar change significantly due to water extraction from the initially wet mortar to the bricks during curing. Numerical simulations reveal the existence of a hydraulic interface resistance between brick and wet/dry cured mortar.

We adopt a classical one-dimensional mathematical model for blood flow in large to medium-sized arteries and veins and study two possible formulations of the equations, a conservative and a non-conservative one. We solve exactly the Riemann problem for both formulations and assess their suitability for various scenarios. In addition we discuss the source terms present in both formulations and investigate their potential stiffness, with the associated numerical complications. Finally, we deploy the high-order ADER approach to solve the equa-tions and point out the efficiency benefits of using modern non-linear methods of very high order of accuracy in both space and time. 1 INTRODUCTION One-dimensional mathematical models are widely ap-plied in cardiovascular modelling, especially for arter-ies [1, 2, 3, 4], to study pressure wave propagation and overall flow characteristics. One-dimensional models offer a valid alternative to both the oversimplified 0D models and the often unaffordable 3D models. More-over, 1D models play a crucial role in more sophisti-cated multi-scale models comprising coupled 0D, 1D and 3D models. In this paper we identify some aspects of 1D models that deserve consideration. This is par-ticularly the case for veins, which compared to arter-ies, have received less attention both from the math-ematical modelling and numerical analysis points of view. This paper is mainly concerned with numerical aspects of one-dimensional models for veins. Back-ground for the steady case is found in the classical works of Shapiro [5] and Pedley et al. [6], for ex-ample. For the time-dependent case see, for instance, Brook et al. [7], Brook and Pedley [8] and more re-cently, Fullana and Zaleski [9] and Marchandise and Flaud [10]. In this paper we adopt a well-known, widely ac-cepted basic mathematical model for one-dimensional blood flow in collapsible tubes and study two main issues: (a) the formulation of the equations and (b) their numerical approximation. On the first issue we re-examine two possible formulations of the equa-tions, namely a conservative and a non-conservative formulation. The latter is generally valid for smooth solutions (eg. no elastic jumps, no contact discontinu-ities) and is widely used. Curiously, these equations can also be expressed in conservation-law form, in

A new two-point boundary value problem algorithm based upon the MATLAB bvp4c package of Kierzenka and Shampine is described. The al- gorithm, implemented in a new package bvp6c, uses the residual control framework of bvp4c (suitably modifled for a more accurate flnite difierence approximation) to maintain a user specifled accuracy. The new package is demonstrated to be as robust as the existing software, but more e-cient for most problems, requiring fewer internal mesh points and evaluations to achieve the required accuracy.

Humidity of indoor air is an important factor influencing the air quality and energy consumption of buildings as well as durability
of building components. Indoor humidity depends on several factors, such as moisture sources, air change, sorption in materials
and possible condensation. Since all these phenomena are strongly dependent on each other, numerical predictions of indoor
humidity need to be integrated into combined heat and airflow simulation tools. The purpose of a recent international collaborative
project, IEA ECBCS Annex 41, has been to advance development in modelling the integral heat, air and moisture transfer processes
that take place in “whole buildings” by considering all relevant parts of its constituents. It is believed that full understanding
of these processes for the whole building is absolutely crucial for future energy optimization of buildings, as this cannot
take place without a coherent and complete description of all hygrothermal processes. This paper will illustrate some of the
modelling work that has taken place within the project and present some of the simulation tools used.

A dynamic mathematical model for simulating the coupled heat and moisture migration through multi-layer porous building materials was proposed. Vapor content and temperature were chosen as the principal driving potentials. The discretization of the governing equations was done by the finite difference approach. A new experimental set-up was also developed in this study. The evolution of transient temperature and moisture distributions inside specimens were measured. The method for determining the temperature gradient coefficient was also presented. The moisture diffusion coefficient, temperature gradient coefficient, sorption–desorption isotherms were experimentally evaluated for some building materials (sandstone and lime-cement mortar). The model was validated by comparing with the experimental data with good agreement. Another advantage of the method lies in the fact that the required transport properties for predicting the non-isothermal moisture flow only contain the vapor diffusion coefficient and temperature gradient coefficient. They are relatively simple, and can be easily determined.

While the transfer equations for moisture and heat in building components are currently undergoing standardisation, atmospheric boundary conditions, conservative modelling and numerical efficiency are not addressed. In a first part, this paper adds a comprehensive description of those boundary conditions, emphasising wind-driven rain and vapour exchange, the main moisture supply and removal mechanism, respectively. In the second part the numerical implementation is tackled, with specific attention to the monotony of the spatial discretisation, and to the mass and energy conservation of the temporal discretisation. Both issues are illustrated with exemplary hygrothermal simulations. Numerical efficiency is treated in two follow-up papers.

This paper presents a review of the role played by trees in the theory of Runge–Kutta methods. The use of trees is in contrast to early publications on numerical methods, in which a deceptively simpler approach was used. This earlier approach is not only non-rigorous, but also incorrect. It is now known, for example, that methods can have different orders when applied to a single equation and when applied to a system of equations; the earlier approach cannot show this. Trees have a central role in the theory of Runge–Kutta methods and they also have applications to more general methods, involving multiple values and multiple stages.

The standardised Glaser method for calculation, prediction and evaluation of moisture performance is considered as rarely applicable. The present state of knowledge, analytical as well as experimental, concerning heat, air and moisture demands updating of standards. This paper presents five numerical benchmark cases for the quality assessment of simulation models for one-dimensional heat, air and moisture (HAM) transfer. In one case, the analytical solution is known and excellent agreement between several solutions from different universities and institutes is obtained. In the remaining four cases, consensus solutions have been found, with good agreement between different HAM models. The work presented here is an outcome of the EU-initiated project for standardisation of HAM calculation methods (HAMSTAD WP2).

A building's durability depends on controlling heat and moisture within its envelope. Moisture diffuses through porous materials that may suffer mould growth and decay (if wood-based) when left moist and warm for too long. Designers try to keep vulnerable components dry, but materials can start to deteriorate before reaching the dew point temperature. Researchers use two-dimensional hygrothermal modeling to calculate time-varying moisture content and temperature at points on a plane through the building envelope thickness. One-dimensional versions of several research programs have been written to assist designers and other building envelope specialists in their work. This paper compares moisture and temperature histories in two building envelopes exposed to a variety of climatic conditions over three years, as calculated by 2D and 1D versions of one such computer program. The 2D calculations come from reports on a methodology for moisture management of wood-frame walls, published in 2003 by a consortium of industry and research partners. Results for a face-sealed stucco wall with rain entry by diffusion only (no seal deficiencies) showed reasonable agreement between 2D and 1D, whereas those for a brick wall with a ventilated air space diverged considerably. With due respect for limitations, 1D simulation can give a first indication of the differences in performance of a wall exposed to different climates, or between different wall assemblies. In some cases the user should consider following up with 2D simulation or field monitoring. La durabilité d'un bâtiment est tributaire du contrôle de la chaleur et de l'humidité à l'intérieur de son enveloppe. L?humidité se diffuse à travers les matériaux poreux, qui peuvent alors subir des dommages par la formation de moisissure et la pourriture (matériaux à base de bois) s?ils demeurent humides et chauds trop longtemps. Bien que les concepteurs tentent de maintenir au sec les composants vulnérables, les matériaux peuvent commencer à se détériorer avant d'atteindre le point de rosée. Les chercheurs utilisent la modélisation hygrothermique bidimensionnelle pour calculer les données de teneur en humidité et de température à valeur temporelle variable en des points dans un plan de l'épaisseur de l'enveloppe de bâtiment. On a écrit des versions unidimensionnelles de plusieurs programmes de recherche afin d'aider les concepteurs et les autres spécialistes des enveloppes de bâtiment dans leur travail. Ce document compare les profils historiques d'humidité et de température de deux (2) enveloppes de bâtiment ayant été exposées à diverses conditions climatiques sur une période de trois (3) années, selon les calculs réalisés au moyen des versions bidimensionnelles et unidimensionnelles d'un programme de ce type. Les calculs bidimensionnels sont issus de rapports sur une méthodologie de contrôle de l'humidité des murs à ossature de bois ayant été publiés en 2003 par un consortium formé de partenaires de l'industrie et du domaine de la recherche. Les résultats obtenus avec un mur de stucco étanchéisé en surface soumis à une pénétration de l'eau de pluie par diffusion seulement (sans aucun manque au niveau de l'étanchéisation) ont révélé une concordance raisonnable entre modélisation bidimensionnelle et modélisation unidimensionnelle. Par contre, les résultats obtenus avec un mur de brique avec un vide d'air ventilé ont divergé considérablement. En prenant bien en compte les limitations implicites à la simulation unidimensionnelle, nous constatons néanmoins que celle-ci peut donner une première indication des différences dans la performance d'un mur exposé à diverses conditions climatiques, ou parmi divers types de murs. Dans certains cas, l'utilisateur devrait envisager de faire suivre cette simulation d'une simulation bidimensionnelle ou d'une surveillance sur les lieux. RES

This paper proposes the use of a Spectral method to simulate diffusive moisture transfer through porous materials as a Reduced-Order Model (ROM). The Spectral approach is an a priori method assuming a separated representation of the solution. The method is compared with both classical Euler implicit and Crank-Nicolson schemes, considered as large original models. Their performance - in terms of accuracy, complexity reduction and CPU time reduction - are discussed for linear and nonlinear cases of moisture diffusive transfer through single and multi-layered one-dimensional domains, considering highly moisture-dependent properties. Results show that the Spectral reduced-order model approach enables to simulate accurately the field of interest. Furthermore, numerical gains become particularly interesting for nonlinear cases since the proposed method can drastically reduce the computer run time, by a factor of 100, when compared to the traditional Crank-Nicolson scheme for one-dimensional applications.

The present work is the hygric characterization of wood fibre insulation boards, using dynamic measurements of relative humidity and sample weight, analyzed in the frame of Bayesian inference for parameter identification under uncertainty. It is an attempt at identifying detailed profiles of moisture-dependent properties, and thus a relatively high number of parameters. Because of this ambition, some caution should be exercised once the outcome of the inversion algorithm is available: in addition to confidence intervals of parameters provided by the Bayesian framework, a simplified form of identifiability analysis is performed by analysing a posteriori parameter correlations and likelihood-based confidence intervals.

Implicit schemes have been extensively used in building physics to compute the solution of moisture diffusion problems in porous materials for improving stability conditions. Nevertheless, these schemes require important sub-iterations when treating nonlinear problems. To overcome this disadvantage, this paper explores the use of improved explicit schemes, such as Dufort–Frankel, Crank–Nicolson and hyperbolization approaches. A first case study has been considered with the hypothesis of linear transfer. The Dufort–Frankel, Crank–Nicolson and hyperbolization schemes were compared to the classical Euler explicit scheme and to a reference solution. Results have shown that the hyperbolization scheme has a stability condition higher than the standard Courant–Friedrichs–Lewy condition. The error of this schemes depends on the parameter τ representing the hyperbolicity magnitude added into the equation. The Dufort–Frankel scheme has the advantages of being unconditionally stable and is preferable for nonlinear transfer, which is the three others cases studies. Results have shown the error is proportional to O(dt). A modified Crank–Nicolson scheme has been also studied in order to avoid sub-iterations to treat the nonlinearities at each time step. The main advantages of the Dufort–Frankel scheme are (i) to be twice faster than the Crank–Nicolson approach; (ii) to compute explicitly the solution at each time step; (iii) to be unconditionally stable and (iv) easier to parallelize on high-performance computer systems. Although the approach is unconditionally stable, the choice of the time discretization remains an important issue to accurately represent the physical phenomena.

Non-Fickian diffusion in native and thermally modified wood was analyzed by the inverse method. A low quality of the identified diffusivity values was found for the diffusivity which was either constant or varying with water content. This was explained by the non-Fickian behavior. It was especially distinct for thermally modified wood for which an increased delay in obtaining the hygroscopic equilibrium was clearly shown. Such a delay was explained by time required for molecular reorganization to produce new sorption sites. This phenomenon was accounted to improve the physical model by modifying the convective boundary condition. A relaxation mechanism was used for this purpose with an adequate time constant.

For a general class of methods, which includes linear multistep and Runge-Kutta methods as special cases, A concept of order relative to a given starting procedure is defined and an order of convergence theorem is proved. The definition is given an algebraic interpretation and illustrated by the derivation of a particular fourth-order method.

Excessive levels of moisture in buildings lead to building pathologies. Moisture also has an impact on the indoor air quality and the hygrothermal comfort of the building's occupants. A comprehensive list of the possible types of damage caused by moisture in buildings is discussed in the present paper. Damage is classified into four types: damage due to the direct action of moisture, damage activated by moisture, damage that occurred in a moist environment and deterioration of the indoor environment. Since moisture pathologies strongly depend on the hygrothermal fields in buildings, integrating these factors into a global model combining heat air and mass transfers and building energy simulation is important. Therefore, the list of moisture damage types is completed with a proposal of factors governing the risk of occurrence of each type of damage. The methodology is experimented on a simple test case combining hygrothermal simulations with the assessment of possible moisture disorders.

Heat and mass transfer between capillary-porous bodies and surrounding incompressible liquid accompanied by a change of phase is not only of theoretical interest but also of great practical importance for some technological processes. Heat and mass transfer inside a porous body (internal heat and mass transfer) also has its unique character. Even now the mechanism of heat and mass transfer in evaporation processes is scantily investigated, and analytical investigations do not, therefore, lead to reliable results. This chapter presents an experimental study of heat and mass transfer in evaporation processes. To elucidate peculiarities of heat transfer with simultaneous mass transfer, a dry body (pure heat transfer) and a moist body (heat transfer in the presence of mass transfer) are investigated. Such a comparison makes it possible to establish relations for interconnected heat and mass transfer processes. In order to describe quantitative relations it is necessary to have a method of analysis which makes it possible to consider the interaction of the heat and mass transfer processes. One such method is the thermodynamics of irreversible processes. The experimental data presented well confirm the mathematical theory of thermodynamics of irreversible transfer processes.

Moisture plays a central role in the provision of healthy buildings, both in relation to indoor humidity levels, which impacts on air quality and thermal comfort, and in relation to interstitial/surface condensation leading to fabric deterioration and mould growth, which impacts on performance and occupant well-being. Integrated building performance simulation (IBPS) provides a means to ensure that due consideration is given to these aspects at the design stage as designers attempt to deploy new approaches to energy demand reduction and sustainable supply. This paper describes how building space and construction moisture flow is modelled within the ESP-r system in a manner that is appropriately coupled to other domain models representing the heat, power, air and light flows within building/plant systems of arbitrary complexity (but with the focus here only on those domains that impact directly on moisture flow). The purpose of the paper is to describe the role of moisture flow modelling within IBPS, the barriers that are likely to be encountered in practice and future development needs. The application of the integrated approach is summarized for the case of mould growth alleviation and the deployment of passive methods for moisture control.

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Water infiltration is known to play an important part in the degradation process of construction materials. Over time, microscopic and macroscopic cracks progressively develop under the effects of mechanical loading and sorption/desorption cycles: their influence is to be accounted for in long-term hygrothermal performance assessments of the building envelope. The present work aims at showing the potential consequences of cracking on the heat and moisture transfer across building facades, in order to justify the need for the identification of damage to prevent durability and thermal issues. Specific simulation cases of insulated and non-insulated building facades were defined, and submitted to atmospheric boundary conditions for simulation times of one month. Some of the simulation geometries included previous measurements of crack patterns in concrete. The comparison of fractured and non-fractured building facades showed the effects of cracks on the moisture accumulation and thermal performance of these wall configurations, thus giving an estimate of what these effects might be in real conditions. A methodology is thus proposed for the identification of renovation needs, which may be applied for the purpose of durability assessments as well.

Deep basements, crawl spaces and slab on grade are typical foundations in residential buildings in North America. The foundation of a house is a somewhat invisible and at sometimes ignored component of the building. Appropriate foundation design and construction practice must not only include thermal performance, but also design for a durable and safe hygrothermal performance.
A hygrothermal simulation tool can be used to evaluate and predict the hygrothermal behavior of an insulated foundation constructions, in cooperation with the surrounding soil. Though, further development of the tool might first be needed and validated to fulfill the prerequisites. Transient hygrothermal simulation tools have existed in Building Science for more than 20 years, but are mainly used for building envelope simulation above ground. A lot of knowledge already exists in Soil Science concerning the variation of the soil material properties in relation to soil texture, moisture content etc. However, Soil Science uses these properties for other purpose and with different modeling approaches, hence a conversion is needed.
This paper studies the existing knowledge of soil properties, converted to apply for simulation in Building Science. Further, the soil properties are implemented in a transient hygrothermal simulation tool, studying the applicability for modeling soil temperature and moisture flow. Finally the results are compared with measurement and followed by a discussion of further investigations and development needed.

The main objective of this work is to present the impact of atmospheric pressure gradient on the hygrothermal transfers in porous material. In this way, a mathematical model described by driving forces of temperature, moisture content and total pressure gradient has been addressed. The non-linear partial differential equations are defined through the balance equations of mass and energy development. After that, a numerical implementation focused on the wood drying behavior is treated for one dimensional Fourier boundary conditions. In order to evaluate the pressure sensitivity, temperature and moisture content profiles are presented and compared to the ones obtained by the classical models 15 and 16. Results show that the atmospheric pressure gradient may cause significant influence on the hygrothermal behavior of the porous materials especially for wood process. A significant effect, up to 15%, on moisture content profile distribution is observed.

The Korteweg-de Vries equation (KdVE) is a classical nonlinear partial differential equation (PDE) originally formulated to model shallow water flow. In addition to the applications in hydrodynamics, the KdVE has been studied to elucidate interesting mathematical properties. In particular, the KdVE balances front sharpening and dispersion to produce solitons, i.e., traveling waves that do not change shape or speed. In this paper, we compute a solution of the KdVE by the method of lines (MOL) and compare this numerical solution with the analytical solution of the kdVE. In a second numerical solution, we demonstrate how solitons of the KdVE traveling at different velocities can merge and emerge. The numerical procedure described in the paper demonstrates the ease with which the MOL can be applied to the solution of PDEs using established numerical approximations implemented in library routines.

In the building science area, mathematical models are developed to provide better indoor thermal comfort with lower energy consumption. Although the fact moisture and air transfer can strongly affect the temperature distribution within constructions, whole-building simulation codes do not take into account the convective air transport in porous materials. In this way, this article presents a heat, air, and moisture (HAM) transfer model based on driving potentials of temperature, air pressure, and water vapor pressure gradients for consolidated porous material in both pendular and funicular states. The solution of the set of governing equations has been simultaneously obtained using the MTDMA (MultiTriDiagonal-Matrix Algorithm) for the three potentials. To conclude, results are presented showing the impact of convective terms on the HAM transfer through a two-layer porous building envelope.

Runge-Kutta methods are applied to the numerical solution of hyperbolic partial differential equations. Conditions that they are locally stable are derived.

A standard for binary floating-point arithmetic is being proposed and there is a very real possibility that it will be adopted by many manufacturers and implemented on a wide range of computers. This development matters to all of us concerned with numerical software. One of the principal motivations for the standard is to distribute more evenly the burden of portability between hardware and software. At present, any program intended to be portable must be designed for a mythical computer that enjoys no capability not supported by every computer on which the program will be run. That mythical computer is so much grubbier than almost any real computer that a portable program will frequently be denigrated as "suboptimal" and then supplanted by another program supposedly "optimal" for the real computer in question but often inferior in critical respects like reliability. A standard --- almost any reasonable standard --- will surely improve the situation. A standard environment for numerical programs will promote fair comparisons and sharing of numerical codes, thereby lowering costs and prices. Furthermore, we have chosen repeatedly to enrich that environment in order that applications programs be simpler and more reliable. Thus will the onus of portability be shared among hardware manufacturers and software producers.

Factors influencing the choice of ODE solver for the numerical solution of PDEs by the method of lines are investigated. The advection—diffusion equation is used to gain insight that is generalized to some classes of nonlinear PDEs. Numerical results for several nonlinear PDEs illustrate the theoretical developments. © 1994 John Wiley & Sons, Inc.

The finite element method is used to analyse heat and mass transfer problems in porous media, in which the thermophysical properties are allowed to vary as functions of temperature and moisture. An example is given of the application of the method to the problem of timber drying.

Drying is a process which involves heat and mass transfer both inside the porous material, where a phase change in moisture occurs from the liquid to the gaseous state, and in the external boundary layer of the convected hot dry air, which heats the porous medium. The equations which govern this process consist of three tightly coupled, highly non-linear partial differential equations for the unknown system variables of moisture content, temperature and pressure. Due to the inherently complex boundary conditions and intricate physical geometries in any practical drying problem, an analytical solution is not possible. In order to obtain a transient drying solution it is necessary to resort to a numerical technique. The numerical solution techniques which were employed in this research were the finite element method and the control volume method. The transient numerical results were compared and contrasted for two timber drying problems, first, at a dry bulb temperature of 50°C, and secondly, at 80°C, both cases being below the boiling point of water.

It is well known that a necessary condition for the Lax-stability of the method of lines is that the eigenvalues of the spatial discretization operator, scaled by the time stepk, lie within a distanceO(k) of the stability region of the time integration formula ask→0. In this paper we show that a necessary and sufficient condition for stability, except for an algebraic factor, is that the ε-pseudo-eigenvalues of the same operator lie within a distanceO(ε)+O(k) of the stability region ask, ε→0. Our results generalize those of an earlier paper by considering: (a) Runge-Kutta and other one-step formulas, (b) implicit as well as explicit linear multistep formulas, (c) weighted norms, (d) algebraic stability, (e) finite and infinite time intervals, and (f) stability regions with cusps.
In summary, the theory presented in this paper amounts to a transplantation of the Kreiss matrix theorem from the unit disk (for simple power iterations) to an arbitrary stability region (for method of lines calculations).

Most building materials are porous, composed of solid matrix and pores. The time varying indoor and outdoor climatic conditions result heat, air and moisture (HAM) transfer across building enclosures. In this paper, a transient model that solves the coupled heat, air and moisture transfer through multilayered porous media is developed and benchmarked using internationally published analytical, numerical and experimental test cases. The good agreements obtained with the respective test cases suggest that the model can be used to assess the hygrothermal performance of building envelope components as well as to simulate the dynamic moisture absorption and release of moisture buffering materials.

In order to precisely predict ground heat transfer, room air temperature and humidity, a combined model has been developed and conceived to calculate both the coupled heat and moisture transfer in soil and floor and the psychrometrics condition of indoor air. The present methodology for the soil is based on the theory of Philip and De Vries, using variable thermophysical properties for different materials. The governing equations were discretized using the finite-volume method and a three-dimensional model for describing the physical phenomena of heat and mass transfer in unsaturated moist porous soils and floor. Additionally, a lumped transient approach for a building room and a finite-volume multi-layer model for the building envelope have been developed to integrate with the soil model. Results are presented in terms of temperature, humidity and heat flux at the interface between room air and the floor, showing the importance of the approach presented and the model robustness for long-term simulations with a high time step.

A mathematical formulation applied to a numerically robust solver is presented, showing that moisture content gradients can be used as driving forces for heat and moisture transport calculation through the interface between porous materials with different pore size distribution functions. For comparison purposes, several boundary conditions are tested—in order to gradually increase the discontinuity effects—and a detailed analysis is undertaken for the temperature and moisture content distributions and sensible and latent heat fluxes, when the discontinuity on the moisture content profile is taken or not into account.

Wind-driven rain (WDR) or driving rain is rain that is given a horizontal velocity component by the wind. WDR research is of importance in a number of research areas including earth sciences, meteorology and building science. Research methods and results are exchangeable between these domains but no exchanges could yet be noted. This paper presents the state-of-the-art of WDR research in building science. WDR is the most important moisture source affecting the performance of building facades. Hygrothermal and durability analysis of facades requires the quantification of the WDR loads. Research efforts can be classified according to the quantification methods used. Three categories are distinguished: (1) experimental methods, (2) semi-empirical methods and (3) numerical methods. The principles of each method are described and the state-of-the-art is outlined. It has been the intent of the present paper to bring together the reports, papers and books—published and unpublished—dealing with WDR research in building science to provide a database of information for researchers interested in and/or working in WDR research, independent of their field of expertise.

This paper gives an onset to whole building hygrothermal modelling in which the interaction between interior and exterior climates via building enclosures is simulated under a moderately cold and humid climate. The focus is particularly on the impact of wind-driven rain (WDR) on the hygrothermal response, mould growth at interior wall surfaces, indoor climate and energy consumption. First the WDR load on the facades of a 4 m × 4 m × 10 m tower is determined. Then the hygrothermal behaviour of the brick walls is analysed on a horizontal slice through the tower. The simulations demonstrate that the impact of WDR loads on the moisture contents in the walls is much larger near the edges of the walls than at the centre. The obtained relative humidity and temperature at the interior wall surfaces are combined with isopleths of generalised spore germination time of fungus mould. The results show that WDR loads can have a significant impact on mould growth especially at the edges of the walls. Finally, for the case analysed, the WDR load causes a significant increase of indoor relative humidity and energy consumption for heating.

The study of moisture migration in materials and building elements is of great importance for the characterization of their behaviour, and affects their durability, waterproofing, degradation and thermal performance. The different mechanisms of moisture transport in building walls and the analysis of interface phenomena have been investigated. Based on the theory proposed by Luikov and Philip—De Vries, a computer program has been developed. The comparison of calculated and measured values obtained by using gamma-ray equipment to measure water content profiles, is considered satisfactory.

Contribution à la modélisation hygrothermique des bâtiments: Application des méthodes de réduction de modèle

- J Berger

J. Berger. Contribution à la modélisation hygrothermique des bâtiments: Application des méthodes
de réduction de modèle. Phd thesis, Université de Grenoble, 2014. 2

- G I M Lucas
- O Müller
- E F Toro

G.I.M. Lucas, O. Müller, E.F. Toro, Some issues in modelling venous haemodynamics, Numer Meth Hyperbolic Equ (2013) 347-354.

Vers une méthode de conception HYGRO-thermique des BATiments performants

- Anr Project

ANR Project HYGRO-BAT. Vers une méthode de conception HYGRO-thermique des BATiments performants, 2014. 26