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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.

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This paper deals with model-order reduction of parametric partial differential equations (PPDE). More specifically, we consider the problem of finding a good approximation subspace of the solution manifold of the PPDE when only partial information on the latter is available. We assume that two sources of information are available: i) a “rough” prior knowledge, taking the form of a manifold containing the target solution manifold; ii) partial linear measurements of the solutions of the PPDE (the term partial refers to the fact that observation operator cannot be inverted). We provide and study several tools to derive good approximation subspaces from these two sources of information. We first identify the best worst-case performance achievable in this setup and propose simple procedures to approximate the corresponding optimal approximation subspace. We then provide, in a simplified setup, a theoretical analysis relating the achievable reduction performance to the choice of the observation operator and the prior knowledge available on the solution manifold. This article is protected by copyright. All rights reserved.

It is of great concern to produce numerically efficient methods for moisture diffusion through porous media, capable of accurately calculate moisture distribution with a reduced computational effort. In this way, model reduction methods are promising approaches to bring a solution to this issue since they do not degrade the physical model and provide a significant reduction of computational cost. Therefore, this article explores in details the capabilities of two model-reduction techniques - the Spectral Reduced-Order Model (Spectral-ROM) and the Proper Generalised Decomposition (PGD) - to numerically solve moisture diffusive transfer through porous materials. Both approaches are applied to three different problems to provide clear examples of the construction and use of these reduced-order models. The methodology of both approaches is explained extensively so that the article can be used as a numerical benchmark by anyone interested in building a reduced-order model for diffusion problems in porous materials. Linear and non-linear unsteady behaviors of unidimensional moisture diffusion are investigated. The last case focuses on solving a parametric problem in which the solution depends on space, time and the diffusivity properties. Results have highlighted that both methods provide accurate solutions and enable to reduce significantly the order of the model around ten times lower than the large original model. It also allows an efficient computation of the physical phenomena with an error lower than 10^{-2} when compared to a reference solution.

Building materials and other materials used in contact with indoor air perform as buffers for humidity excitations and can therefore potentially alleviate moisture problems in the indoor environment. A recent NORDTEST project defines a so-called Moisture Buffer Value which should be used as an unequivocal measure to characterize this property of building materials. The paper explains the property and gives an outline of the test protocol as it is described in a NORDTEST Method. The paper gives details of application of the new property in building design to achieve buildings with good indoor air quality and minimal energy consumption.

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.

The Burger's equation serves as a useful mathematical model to be applied in fluid dynamic problems. Besides, this equation is often used to test and compare numerical techniques. In the present paper, the numerical solutions determined by both the finite volume method (FVM) and the Fourier pseudospectral method (FPM), and the results are compared with the analytical, exact solution. Furthermore, performance in obtaining the results is properly reported. The analysis includes periodic and non-periodic domains, for both methods. The nonlinear term in the FVM, is discretion by using upwind and central-differencing schemes, showing a rate of convergence for the second-order accurate. Due requirement of the domains in FPM to be periodic, in the present work, the immersed boundary methodology is used, to solve the equation at non-periodic domains. It will also be shown that this approach damages the accuracy and the rate convergence of the FPM.

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.

An important factor in soil heat transfer that is often over looked is the effect of moisture, which can vary the effective thermal conductivity by a factor of ten. The objective of this research was to investigate the ground-coupled heat and moisture transfer from buildings, and to develop results and tools to improve energy simulation of ground-coupled heat transfer.

The modelling of heat and mass transfer in wet porous media in the presence of evaporation-condensation is revisited by using the homogenization method of asymptotic expansions for periodic structures. In order to produce the ‘upscaled’ equations for the continuum equivalent to the porous medium, we start from the pore level. At this scale the physics is described by convection and Fick's molecular diffusion coupled with heat transfer. The phase change process is incorporated into the analysis. The main advantage of the method is to use a systematic, rigorous and unified treatment to provide a general comprehension of all the interactions involved by the different heat and mass transfers. Four characteristic selected models are carried out. Their domains of validity are determined in function of the relative weight of the different phenomena in presence. Comparison with other models in the literature is presented. It appears that some of them exhibit a similar structure. In particular, the continuous passage between the different macroscopic models is investigated. Finally, the condition for a non-homogenizable situation, i.e., when it is impossible to find a macroscopic equivalent description is also addressed.

In calculations of building heat loss via the ground, the coupling with soil moisture transfer is generally ignored, an important hypothesis which will be falsified in this paper. Results from coupled simulations – coupled soil heat and moisture transfer equations and complete surface heat and moisture balances – are compared to results from linear simulations. It is shown that the coupled calculations give notably higher heat losses. Surface temperature, the driving force for heat loss via the ground, is identified as a first important source for these deviations: it is shown that while the averages of the surface temperature are almost equal in coupled and linear calculations, the amplitude in the coupled simulation is considerably higher. A further study reveals that variation of the thermal properties with moisture content also contributes partially to the observed differences. Transfer and storage of sensible heat linked to moisture in the liquid phase was shown to be the last important influencing factor.

It is well known that thermal insulation is a leading strategy for reducing energy consumption associated to heating or cooling processes in buildings. Nevertheless, building insulation can generate high expenditures so that the selection of an optimum insulation thickness requires a detailed energy simulation as well as an economic analysis. In this way, the present study proposes an innovative non-uniform adaptive method to determine the optimal insulation thickness of external walls. First, the method is compared with a reference solution to properly understand the features of the method, which can provide high accuracy with less spatial nodes. Then, the adaptive method is used to simulate the transient heat conduction through the building envelope of buildings located in Brazil, where there is a large potential of energy reduction. Simulations have been efficiently carried out for different wall and roof configurations, showing that the innovative method efficiently provides a gain of 25% on the computer run time.

This book intends to stimulate research in simulation of diffusion problems in building physics, by first providing an overview of mathematical models and numerical techniques such as the finite difference and finite-element methods traditionally used in building simulation tools. Then, nonconventional methods such as reduced order models, boundary integral approaches and spectral methods are presented, which might be considered in the next generation of building-energy-simulation tools. The advantage of these methods includes the improvement of the numerical solution of diffusion phenomena, especially in large domains relevant to building energy performance analysis.

This work presents an efficient numerical method based on spectral expansions for simulation of heat and moisture diffusive transfers through multilayered porous materials.
Traditionally, by using the finite-difference approach, the problem is discretized in time and
space domains (Method of lines) to obtain a large system of coupled Ordinary Differential
Equations (ODEs), which is computationally expensive. To avoid such a cost, this paper
proposes a reduced-order method that is faster and accurate, using a much smaller system of ODEs. To demonstrate the benefits of this approach, tree case studies are presented. The first one considers nonlinear heat and moisture transfer through one material layer. The second case - highly nonlinear - imposes a high moisture content gradient - simulating a rain like condition - over a two-layered domain, while the last one compares the numerical prediction against experimental data for validation purposes. Results show how the nonlinearities and the interface between materials are easily and naturally treated with the spectral reduced-order method. Concerning the reliability part, predictions show a good agreement with experimental results, which confirm robustness, calculation efficiency and high accuracy of the proposed approach for predicting the coupled heat and moisture transfer through porous materials.

A computational procedure known as co-simulation has been proposed in the literature as a possibility to extend the capabilities and improve the accuracy of building performance simulation (BPS) tools. Basically, the strategy relies on the data exchanging between the BPS and a specialized software, where specific physical phenomena are simulated more accurately thanks to a more complex model, where advanced physics are taken into account. Among many possibilities where this technique can be employed, one could mention airflow, three-dimensional heat transfer or detailed HVAC systems simulation, which are commonly simplified in BPS tools. When considering complex models available in specialized software, the main issue of the co-simulation technique is the considerable computational effort demanded. This paper proposes a new methodology for time-consuming simulations with the purpose of challenging this particular issue. For a specific physical phenomenon, the approach consists of designing a new model, called prediction model, capable to provide results, as close as possible to the ones provided by the complex model, with a lower computational run time. The synthesis of the prediction model is based on artificial intelligence, being the main novelty of the paper. Basically, the prediction model is built by means of a learning procedure, using the input and output data of co-simulation where the complex model is being used to simulate the physics. Then the synthesized prediction model replaces the complex model with the purpose of reducing significantly the computational burden with a small impact on the accuracy of the results. Technically speaking, the learning phase is performed using a machine learning technique, and the model investigated here is based on a recurrent neural network model and its features and performance are investigated on a case study, where a single-zone house with a triangular prism-shaped attic model is co-simulated with both CFX (CFD tool) and Domus (BPS tool) programs. Promising results lead to the conclusion that the proposed strategy enables to bring the accuracy of advanced physics to the building simulation field – using prediction models – with a much reduced computational cost. In addition, re-simulations might be run solely with the already designed prediction model, demanding computer run times even lower than the ones required by the lumped models available in the BPS tool.

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.

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.

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.

A novel approach is presented to constrain reduced-order models (ROM) based on proper orthogonal decomposition (POD). The Karush-Kuhn-Tucker (KKT) conditions were applied to the traditional reduced-order model to constrain the solution to user-defined bounds. The constrained reduced-order model (C-ROM) was applied and validated against the analytical solution to the first-order wave equation. C-ROM was also applied to the analysis of fluidized beds. It was shown that the ROM and C-ROM produced accurate results and that C-ROM was less sensitive to error propagation through time than the ROM.

Implicit schemes require important sub-iterations when dealing with highly nonlinear problems such as the combined heat and moisture transfer through porous building elements. The computational cost rises significantly when the whole-building is simulated, especially when there is important coupling among the building elements themselves with neighbouring zones and with HVAC (Heating Ventilation and Air Conditioning) systems. On the other hand, the classical Euler explicit scheme is generally not used because its stability condition imposes very fine time discretisation. Hence, this paper explores the use of an improved explicit approach - the Dufort-Frankel scheme - to overcome the disadvantage of the classical explicit one and to bring benefits that cannot be obtained by implicit methods. The Dufort-Frankel approach is first compared to the classical Euler implicit and explicit schemes to compute the solution of nonlinear heat and moisture transfer through porous materials. Then, the analysis of the Dufort-Frankel unconditionally stable explicit scheme is extended to the coupled heat and moisture balances on the scale of a one- and a two-zone building models. The Dufort-Frankel scheme has the benefits of being unconditionally stable, second-order accurate in time O(dt^2) and to compute explicitly the solution at each time step, avoiding costly sub-iterations. This approach may reduce the computational cost by twenty, as well as it may enable perfect synchronism for whole-building simulation and co-simulation.

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.

The flow control constitutes a challenging research topic with numerous applications in aeronautics, aerodynamics, fluid mechanics, civil engineering, and so on. Due to the use of iterative algorithms, it is costly in both CPU time and memory requirements. In this paper, an optimal control strategy with reduced-order model built with proper orthogonal decomposition approach is proposed. The methodology is developed to control an anisothermal flow in a lid-driven cavity with one control parameter and then extended to at two control parameters. The control is realized in quasi-real time, which opens the way to promising practical applications.

This paper proposes a full grid interval collocation method (FGICM) and a sparse grid interval collocation method (SGICM) to solve the uncertain heat convection-diffusion problem with interval input parameters in material properties, applied loads and boundary conditions. The Legendre polynomial series is adopted to approximate the functional dependency of temperature response with respect to the interval parameters. In the process of calculating the expansion coefficients, FGICM evaluates the deterministic solutions directly on the full tensor product grids, while the Smolyak sparse grids are reconstructed in SGICM to avoid the curse of dimensionality. The eventual lower and upper bounds of temperature responses are easily predicted based on the continuously-differentiable property of the approximate function. Comparing results with traditional Monte Carlo simulations and perturbation method, the numerical example evidences the remarkable accuracy and effectiveness of the proposed methods for interval temperature field prediction in engineering.

In this paper, the proper generalized decomposition (PGD) is used for model reduction in the solution of an inverse heat conduction problem within the Bayesian framework. Two PGD reduced order models are proposed and the approximation Error model (AEM) is applied to account for the errors between the complete and the reduced models. For the first PGD model, the direct problem solution is computed considering a separate representation of each coordinate of the problem during the process of solving the inverse problem. On the other hand, the second PGD model is based on a generalized solution integrating the unknown parameter as one of the coordinates of the decomposition. For the second PGD model, the reduced solution of the direct problem is computed before the inverse problem within the parameter space provided by the prior information about the parameters, which is required to be proper. These two reduced models are evaluated in terms of accuracy and reduction of the computational time on a transient three-dimensional two region inverse heat transfer problem. In fact, both reduced models result on substantial reduction of the computational time required for the solution of the inverse problem, and provide accurate estimates for the unknown parameter due to the application of the approximation error model approach.

In this paper, detailed numerical calculations of the spectral collocation method (SCM) to simulate natural convection in a square porous cavity using two different local thermal models, i.e., the local thermal equilibrium model and the local thermal non-equilibrium model, are presented and formulated. In this approach, stream function and temperature are approximated by the Chebyshev polynomials and the dimensionless governing equations are discretized by the Chebyshev–Gauss–Lobatto collocation points. The two step method, i.e., the matrix diagonalization method, is used to solve the discretized equations. The present results are compared with those reported in literature. It is found that these results are in excellent agreement. Furthermore, the exact solutions for local thermal equilibrium model have been constructed to test the accuracy of the method, and it can be observed from the test that the Chebyshev spectral collocation method can produce high accuracy. Meanwhile, the isotherms and the streamlines are analyzed to reveal the fluid flow and heat transfer for various parameters, i.e., the Rayleigh number, the inter-phase heat transfer coefficient, and the thermal conductivity ratio.

Presents introductory skills needed for prediction of heat transfer and fluid flow, using the numerical method based on physical considerations. The author begins by discussing physical phenomena and moves to the concept and practice of the numerical solution. The book concludes with special topics and possible applications of the method.

In the present study we consider an example of a boundary value problem for a simple second order ordinary differential equation, which may exhibit a boundary layer phenomenon depending on the value of a free parameter. To this equation we apply an adaptive numerical method on redistributed grids. We show that usual central finite differences, which are second order accurate on a uniform grid, can be substantially upgraded to the fourth order by a suitable choice of the underlying non-uniform grid. Moreover, we show also that some other choices of the nodes distributions lead to substantial degradation of the accuracy. This example is quite pedagogical and we use it only for illustrative purposes. It may serve as a guidance for more complex problems.

In the present article we describe a few simple and efficient finite volume type schemes on moving grids in one spatial dimension. The underlying finite volume scheme is conservative and it is accurate up to the second order in space. The main novelty consists in the motion of the grid. This new dynamic aspect can be used to resolve better the areas with high solution gradients or any other special features. No interpolation procedure is employed, thus an unnecessary solution smearing is avoided. Thus, our method enjoys excellent conservation properties. The resulting grid is completely redistributed according the choice of the so-called monitor function. Several more or less universal choices of the monitor function are provided. Finally, the performance of the proposed algorithm is illustrated on several examples stemming from the simple linear advection to the simulation of complex shallow water waves.

A Chebyshev collocation spectral method based on modified discrete ordinates method (SP-MDOM) is developed for radiative heat transfer problems to remedy the ray effect. The media analyzed are absorbing, emitting and isotropic or anisotropic scattering. The radiative transfer equation (RTE) is decomposed into two parts: the wall-related intensity and the medium-related intensity. The former is solved analytically. For the latter, the discrete ordinates method is used for angularly discretization with quadrature scheme and then solved by Chebyshev collocation spectral method (CSM). In this study, the 2-D rectangular enclosures as well as the partitioned domain with different boundary conditions and optical parameters are considered. The domain decomposition concept is used along with the SP-MDOM to handle the radiative transfer in partitioned domain. The accuracy of the results obtained by the SP-MDOM is assessed by comparing the predictions with those obtained by other researchers. The results confirm the capability of the SP-MDOM to remedy the nonphysical anomalies caused by the ray effect.

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.

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 an a priori model 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 model Delphin in 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.

A theory of moisture movement in porous, materials under temperature gradients is developed which explains apparently discordant experimental information, including (a) the large value of the apparent vapor transfer, (b) effect of moisture content on net moisture transfer, and (c) the transfer of latent heat by distillation. The previous simple theory of water vapor diffusion in porous media under temperature gradients neglected the interaction of vapor, liquid and solid phases, and the difference between average temperature gradient in the air‐filled pores and in the soil as a whole. With these factors taken into account, an (admittedly approximate) analysis is developed which predicts orders of magnitude and general behavior in satisfactory agreement with the experimental facts. An important implication of the present approach is that experimental methods used to distinguish between liquid and vapor transfer have not done so, since what has been supposed to be vapor transfer has actually been series‐parallel flow through liquid ‘islands’ located in a vapor continuum. Equations describing moisture and heat transfer in porous materials under combined moisture and temperature gradients are developed. Four moisture‐dependent diffusivities arising in this connection are discussed briefly.

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.

Numerical modeling of the ground heat exchangers requires important computational resources to accurately reproduce the short-time thermal responses over a long-time period. Considering geometries of the vertical ground heat exchanger, domain decomposition is proposed in the vertical and horizontal directions. As the principal direction of the heat transfer in such a system is horizontal and here the cumbersome finite element method in treating the domain decomposition is adopted, only the horizontal soil domain case is investigated in this work. A new type of boundaries to decomposed sub-zones is proposed, and then a restitution method is developed to keep all the matrix terms inherent in initial matrices ahead of decomposition. The state model size reduction technique is used for each sub-zone model to reduce the model size, and then the reduced models are regrouped into a single state model using the new proposed coupling method. Results show that the developed decomposition and coupling methods are pertinent with negligible errors (less than 0.005 °C for the maximum), and the final reduced model gives acceptable results for typical purposes of geothermal simulations. From some sensitivity tests, it is found that accuracy of the reduced model can be systematically improved by increasing the reduced order or the number of sub-zones. The proposed model is remarkably faster than the reference model (more than 300 times), implying that a detailed 3-D numerical model can be used for long-time simulations.

Thermal radiation transfer in one-dimensional parallel plates and two-dimensional rectangle enclosures filled with non-gray gases, namely CO2, H2O, or their mixtures, is calculated using the spectral collocation method with full spectrum k-distribution model (SCM–FSK). The k-distribution model is a promising model for treating the spectral properties of an absorbing–emitting medium, representing an alternative to line-by-line calculations which reduces the number of radiative transfer equation (RTE) evaluations from the order of a million to the order of ten without any significant loss of accuracy. Moreover, the full spectrum k-distribution model, as a global model, can be easily combined with other numerical methods to solve the RTE. The spectral collocation method (SCM) which is used to solve partial differential equations is combined with FSK for the present problems. In order to test the accuracy and efficiency of SCM–FSK, several gas radiation transfer problems involving isothermal/non-isothermal and homogeneous/inhomogeneous non-gray gases are examined. The results obtained by SCM–FSK are assessed by comparing the predictions with line by line results. These comparisons indicate that SCM–FSK is sufficiently accurate and convenient for engineering calculations.

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.

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.

The equations governing the transfer of heat and mass in a partially saturated soil are presented and solved numerically. A parametric study showing the effect of various terms on the distributions of temperature and moisture within the soil are given.

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.