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This work deals with an inverse two-dimensional nonlinear heat conduction problem to determine the top and lateral surface transfer coefficients. For this, the \textsc{B}ayesian framework with the \textsc{M}arkov Chain \textsc{M}onte \textsc{C}arlo algorithm is used to determine the posterior distribution of unknown parameters. To handle the computational burden, a lumped one-dimensional model is proposed. The lumped model approximations are considered within the parameter estimation procedure thanks to the Approximation Error Model. The experiments are carried out for several configurations of chamber ventilator speed. Experimental observations are obtained through a complete measurement uncertainty propagation. By solving the inverse problem, accurate probability distributions are determined. Additional investigations are performed to demonstrate the reliability of the lumped model, in terms of accuracy and computational gains.

Within the environmental context, numerical modeling is a promising approach to assessing the energy efficiency of buildings. Resilient buildings need to be designed, and 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 usual. The model enables computing parametric solutions using basis interpolation on the tangent space of the \textsc{Grassmann} manifold. Three study cases are considered to verify the efficiency of the \revision{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 \revision{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.

The estimation of wall thermal properties by \emph{in situ} measurement enables to increase the reliability of the model predictions for building energy efficiency. Nevertheless, retrieving the unknown parameters has an important computational cost. Indeed, several computations of the heat transfer problem are required to identify these thermal properties. To handle this drawback, an innovative approach is investigated. The first step is to search the optimal experiment design among the sequence of observation of several months. A reduced sequence of observations of three days is identified which guarantees to estimate the parameter with the maximum accuracy. Moreover, the inverse problem is only solved for this short sequence. To decrease further the computational efforts, a reduced order model based on the modal identification method is employed. This \emph{a posteriori} model reduction method approximates the solution with a lower degree of freedom. The whole methodology is illustrated to estimate the thermal diffusivity of an historical building that has been monitored with temperature sensors for several months. The computational efforts is cut by five. The estimated parameter improves the reliability of the predictions of the wall thermal efficiency.

The \emph{in situ} estimation of the thermal properties of existing building wall materials is a computationally expensive procedure. Its cost is highly proportional to the duration of measurements. To decrease the computational cost a methodology using a D-optimum criterion to select an optimal experiment duration is proposed. This criterion allows to accurately estimate the thermal properties of the wall using a reduced measurement plan. The methodology is applied to estimate the thermal conductivity of the three-layer wall of a historical building in France. Three different experiment sequences (one, three and seven days) and three spatial distributions of the thermal conductivity are investigated. Then using the optimal duration of observations the thermal conductivity is estimated using the hybrid optimization method. Results show a significant reduction of computational time; and reliable simulation of physical phenomena using the estimated values.

Within the framework of building energy assessment, this article proposes to use a derivative based sensitivity analysis of heat transfer models in a building envelope. Two, global and local, estimators are obtained at low computational cost, to evaluate the influence of the parameters on the model outputs. Ranking of these estimators values allows to reduce the number of model unknown parameters by excluding non-significant parameters. A comparison with variance and regression-based methods is carried out and the results highlight the satisfactory accuracy of the continuous-based approach. Moreover, for the carried investigations the approach is $100$ times faster compared to the variance-based methods. A case study applies the method to a real-world building wall. The sensitivity of the thermal loads to local or global variations of the wall thermal is investigated. Additionally, a case study of wall with window is analyzed.

A two-dimensional model is proposed for energy efficiency assessment through the simulation of heat transfer in building envelopes, considering the influence of the surrounding environment. The model is based on the \DF ~approach that provides an explicit scheme with a relaxed stability condition. The model is first validated using an analytical solution and then compared to three other standard schemes. Results show that the proposed model offers a good compromise in terms of high accuracy and reduced computational efforts. Then, a more complex case study is investigated, considering non-uniform shading effects due to the neighboring buildings. In addition, the surface heat transfer coefficient varies with wind velocity and height, which imposes an addition non-uniform boundary condition. After showing the reliability of the model prediction, a comparison over almost $120$ cities in France is carried out between the two- and the one-dimensional approaches of the current building simulation programs. Important discrepancies are observed for regions with high magnitudes of solar radiation and wind velocity. Last, a sensitivity analysis is carried out using a derivative-based approach. It enables to assess the variability of the solution according to the modeling of the two-dimensional boundary conditions. Moreover, the proposed model computes efficiently the solution and its sensitivity to the modeling of the urban environment.

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.

Within the environmental context, several tools based on simulations have been proposed to analyze the physical phenomena of heat and mass transfer in porous materials. However, it is still an open challenge to propose tools that do not require to perform computations to catch the dominant processes. Thus, this article proposes to explore advantages of using a dimensionless analysis by scaling the governing equations of heat and mass transfer. Proposed methodology introduces dimensionless numbers and their nonlinear distortions. The relevant investigation enables to enhance the preponderant phenomena to \emph{(i)} compare different categories of materials, \emph{(ii)} evaluate the competition between heat and mass transfer for each material or \emph{(iii)} describe the transfer in multi-layered wall configurations. It also permits to define hygrothermal kinetic, geometric and dynamic similarities among different physical materials. Equivalent systems can be characterized in the framework of experimental or wall designs. Three cases are presented for similarity studies in terms of \emph{(i)} equivalent material length, \emph{(ii)} time of heat and mass transfer and \emph{(iii)} experimental configurations. All these advantages are illustrated in the given article considering $49$ building materials separated in $7$ categories.

The design of numerical tools to model the behavior of building materials is a challenging task. The crucial point is to save computational cost and maintain high accuracy of predictions. There are two main limitations on the time scale choice, which put an obstacle to solve the above issues. First one is the numerical restriction. A number of research is dedicated to overcome this limitation and it is shown that it can be relaxed with innovative numerical schemes. The second one is the physical restriction. It is imposed by properties of a material, phenomena itself and corresponding boundary conditions. This work is focused on the study of a methodology that enables to overcome the physical restriction on the time grid. So-called Average Reduced Model (ARM) is suggested. It is based on smoothing the time-dependent boundary conditions. Besides, the approximate solution is decomposed into average and fluctuating components. The primer is obtained by integrating the equations over time, whereas the latter is an user-defined empirical model. The methodology is investigated for both heat diffusion and coupled heat and mass transfer. It is demonstrated that the signal core of the boundary conditions is preserved and the physical restriction can be relaxed. The model proved to be reliable, accurate and efficient also in comparison with the experimental data of two years. The implementation of the scarce time-step of $1 \, \sf{h}$ is justified. It is shown, that by maintaining the tolerable error it is possible to cut computational effort up to almost four times in comparison with the complete model with the same time grid.

The sorption curve is an essential feature for the modelling of heat and mass transfer in porous building materials. Several models have been proposed in the literature to represent the amount of moisture content in the material according to the water activity (or capillary pressure) level. These models are based on analytical expressions and few parameters that need to be estimated by inverse analysis. This article investigates the reliability of eight models through the accuracy of the estimated parameters. For this, experimental data for a wood fibre material are generated with special attention to the stop criterion to capture long time kinetic constants. Among five sets of measurements, the best estimate is computed. The reliability of the models is then discussed. After proving the theoretical identifiability of the unknown parameters for each model, the primary identifiability is analysed. It evaluates whether the parameters influence on the model output is sufficient to proceed the parameter estimation with accuracy. For this, a continuous derivative-based approach is adopted. Seven models have a low primary identifiability for at least one parameter. Indeed, when estimating the unknown parameters using the experimental observations, the parameters with low primary identifiability exhibit large uncertainties. Finally, an Approximation Bayesian Computation algorithm is used to simultaneously select the best model and estimate the parameters that best represent the experimental data. The thermodynamic and \textsc{Feng}--\textsc{Xing} models, together with a proposed model in this work, were the best ones selected by this algorithm.

Innovative numerical scheme studied in this work enables to overcome two main limitations of Building Performance Simulation (BPS) programs as high computational cost and the choice of a very fine numerical grid. The method, called Super-Time-Stepping (STS), is novel to the state-of-the-art of building simulations, but has already proved to be sufficiently efficient in recent studies from anisotropic heat conduction in astrophysics (Meyer et al. 2014). The given research is focused on employment of this adopted numerical method to model drying of a rammed earth wall with an additional insulation layer. The results show considerable advantage of the STS method compared to standard Euler explicit scheme. It is possible to choose at least 100 times bigger time-steps to maintain high accuracy and to cut computational cost by more than 92% in the same time., Comment: 10 pages, 6 figures, 4 tables, 14 references. Other author's papers can be downloaded at http://www.denys-dutykh.com/

Predictions of physical phenomena in buildings are carried out by using physical models formulated as a mathematical problem and solved by means of numerical methods, aiming at evaluating, for instance, the building thermal or hygrothermal performance by calculating distributions and fluxes of heat and moisture transfer. Therefore, the choice of the numerical method is crucial since it is a compromise among (i) the solution accuracy, (ii) the computational cost to obtain the solution and (iii) the complexity of the method implementation. An efficient numerical method enables to compute an accurate solution with a minimum computational run time (CPU). On that account, this article brings an investigation on the performance of three numerical methods. The first one is the standard and widely used finite-difference approach, while the second one is the so-called RC approach, which is a particular method brought to the building physics area by means of an analogy of electric circuits. The third numerical method is the spectral one, which has been recently proposed to solve nonlinear diffusive problems in building physics. The three methods are evaluated in terms of accuracy on the assessment of the dependent variable (temperature or vapor pressure) or of density of fluxes for three different cases: i) heat diffusion through a concrete slab, ii) moisture diffusion through an aerated concrete slab and iii) heat diffusion using measured temperatures as boundary conditions. Results highlight the spectral approach as the most accurate method. The RC based model with a few number of resistances does not provide accurate results for temperature and vapor pressure distributions neither to flux densities nor conduction loads., Comment: 35 pages, 19 figures, 2 tables, 42 references. Other author's papers can be downloaded at http://www.denys-dutykh.com/

The fidelity of a model relies both on its accuracy to predict the physical phenomena and its capability to estimate unknown parameters using observations. This article focuses on this second aspect by analyzing the reliability of two mathematical models proposed in the literature for the simulation of heat losses through building walls. The first one, named DuFort-Frankel (DF), is the classical heat diffusion equation combined with the DuFort-Frankel numerical scheme. The second is the so-called RC lumped approach, based on a simple ordinary differential equation to compute the temperature within the wall. The reliability is evaluated following a two stages method. First, samples of observations are generated using a pseudo-spectral numerical model for the heat diffusion equation with known input parameters. The results are then modified by adding a noise to simulate experimental measurements. Then, for each sample of observation, the parameter estimation problem is solved using one of the two mathematical models. The reliability is assessed based on the accuracy of the approach to recover the unknown parameter. Three case studies are considered for the estimation of (i) the heat capacity, (ii) the thermal conductivity or (iii) the heat transfer coefficient at the interface between the wall and the ambient air. For all cases, the DF mathematical model has a very satisfactory reliability to estimate the unknown parameters without any bias. However, the RC model lacks of fidelity and reliability. The error on the estimated parameter can reach 40% for the heat capacity, 80% for the thermal conductivity and 450% for the heat transfer coefficient., Comment: 29 pages, 20 figures, 4 tables, 1 appendix, 29 references. Other author's papers can be downloaded at http://www.denys-dutykh.com/

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., Comment: 46 pages, 12 figures, 3 tables, 46 references. Other author's papers can be downloaded at http://www.denys-dutykh.com/

The goal of this study is to propose an efficient numerical model for the predictions of capillary adsorption phenomena in a porous material. The Scharfetter-Gummel numerical scheme is proposed to solve an advection-diffusion equation with gravity flux. Its advantages such as accuracy, relaxed stability condition, and reduced computational cost are discussed along with the study of linear and nonlinear cases. The reliability of the numerical model is evaluated by comparing the numerical predictions with experimental observations of liquid uptake in bricks. A parameter estimation problem is solved to adjust the uncertain coefficients of moisture diffusivity and hydraulic conductivity., Comment: 41 pages, 19 figures, 3 tables, 35 references. Other author's papers can be downloaded at http://www.denys-dutykh.com/

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., Comment: 36 pages, 18 figures, 6 tables, 42 references. Other author's papers can be downloaded at http://www.denys-dutykh.com/

This work presents an alternative view on the numerical simulation of diffusion processes applied to the heat and moisture transfer through 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). Thus, 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 methods of high order. To demonstrate the benefits of this new approach, three case studies are presented, in which one of them is compared with experimental data. The first one considers nonlinear heat and moisture transfer through one material layer while the second one considers two material layers. Results show how the nonlinearities and the interface between materials are easily treated, by reasonably using a fourth-order adaptive method. Finally, the last case study compares numerical results with experimental measurements, showing a good agreement., Comment: 45 pages, 21 figures, 5 tables, 47 references. Other author's papers can be downloaded at http://www.denys-dutykh.com/

Comparisons of experimental observation of heat and moisture transfer through porous building materials with numerical results have been presented in numerous studies reported in literature. However, some discrepancies have been observed, highlighting underestimation of sorption process and overestimation of desorption process. Some studies intend to explain the discrepancies by analysing the importance of hysteresis effects as well as carrying out sensitivity analyses on the input parameters as convective transfer coefficients. This article intends to investigate the accuracy and efficiency of the coupled solution by adding advective transfer of both heat and moisture in the physical model. In addition, the efficient Scharfetter and Gummel numerical scheme is proposed to solve the system of advection-diffusion equations, which has the advantages of being well-balanced and asymptotically preserving. Moreover, the scheme is particularly efficient in terms of accuracy and reduction of computational time when using large spatial discretisation parameters. Several linear and non-linear cases are studied to validate the method and highlight its specific features. At the end, an experimental benchmark from the literature is considered. The numerical results are compared to the experimental data for a pure diffusive model and also for the proposed model. The latter presents better agreement with the experimental data. The influence of the hysteresis effects on the moisture capacity is also studied, by adding a third differential equation., Comment: 51 pages, 21 figures, 3 tables, 44 references. Other author's publications can be downloaded at http://www.denys-dutykh.com/

The reliability of a model is its accuracy in predicting the physical phenomena using the known input parameters. It also depends on the model's ability to estimate relevant parameters using observations of the physical phenomena. In this paper, the reliability of the VTT model is investigated under these two criteria for various given temperature and relative humidity constant in time. First of all, experiments are conducted on bamboo fiberboard. Using these data, five parameters of the VTT model, defining the mold vulnerability class of a material, are identified. The results highlight that the determined parameters are not within the range of the classes defined in the VTT model. In addition, the quality of the parameter estimation is not satisfactory. Then the sensitivity of the numerical results of the VTT model is analyzed by varying an input parameter. These investigations show that the VTT mathematical formulation of the physical model of mold growth is not reliable. An improved model is proposed with a new mathematical formulation. It is inspired by the logistic equation whose parameters are estimated using the experimental data obtained. The parameter estimation is very satisfactory. In the last parts of the paper, the numerical predictions of the improved model are compared to experimental data from the literature to prove its reliability., Comment: 33 pages, 10 figures, 9 tables, 29 references. Other author's papers can be downloaded at http://www.denys-dutykh.com/

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., Comment: 42 pages, 14 figures, 1 table, 69 references. Other author's papers can be downloaded at http://www.denys-dutykh.com/. arXiv admin note: text overlap with arXiv:1704.07607

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., Comment: 42 pages, 22 figures, 2 tables, 51 references. Other author's papers can be downloaded at http://www.denys-dutykh.com/

This paper deals with an inverse problem applied to the field of building physics to experimentally estimate three sorption isotherm coefficients of a wood fiber material. First, the mathematical model, based on convective transport of moisture, the Optimal Experiment Design (OED) and the experimental set-up are presented. Then measurements of relative humidity within the material are carried out, after searching the OED, which is based on the computation of the sensitivity functions and a priori values of the unknown parameters employed in the mathematical model. The OED enables to plan the experimental conditions in terms of sensor positioning and boundary conditions out of 20 possible designs, ensuring the best accuracy for the identification method and, thus, for the estimated parameter. Two experimental procedures were identified: i) single step of relative humidity from 10% to 75% and ii) multiple steps of relative humidity 10-75-33-75% with an 8-day duration period for each step. For both experiment designs, it has been shown that the sensor has to be placed near the impermeable boundary. After the measurements, the parameter estimation problem is solved using an interior point algorithm to minimize the cost function. Several tests are performed for the definition of the cost function, by using the L^2 or L^\infty norm and considering the experiments separately or at the same time. It has been found out that the residual between the experimental data and the numerical model is minimized when considering the discrete Euclidean norm and both experiments separately. It means that two parameters are estimated using one experiment while the third parameter is determined with the other experiment. Two cost functions are defined and minimized for this approach. Moreover, the algorithm requires less than 100 computations of the direct model to obtain the solution. In addition, the OED sensitivity functions enable to capture an approximation of the probability distribution function of the estimated parameters. The determined sorption isotherm coefficients calibrate the numerical model to fit better the experimental data. However, some discrepancies still appear since the model does not take into account the hysteresis effects on the sorption capacity. Therefore, the model is improved proposing a second differential equation for the sorption capacity to take into account the hysteresis between the main adsorption and desorption curves. The OED approach is also illustrated for the estimation of five of the coefficients involved in the hysteresis model. To conclude, the prediction of the model with hysteresis are compared with the experimental observations to illustrate the improvement of the prediction., Comment: 51 pages, 20 figures, 4 tables and 56 references. Other author's papers can be downloaded at http://www.denys-dutykh.com/

This paper presents a practical application of the concept of Optimal Experiment Design (OED) for the determination of properties of porous materials with in-situ measurements and an identification method. First, an experimental set-up was presented and used for the measurement of relative humidity within a wood fibre material submitted to single and multiple steps of relative humidity variation. Then, the application of OED enabled to plan the experimental conditions in terms of sensor positioning and boundary conditions out of 20 possible designs. The OED search was performed using the Fisher information matrix and a priori knowledge of the parameters. It ensures to provide the best accuracy of the identification method and thus the estimated parameter. Optimal design results have been found for single steps from the relative humidity phi = 10 to 75%, with one sensor located at the position X between 4 and 6 cm, for the estimation of moisture permeability coefficients, while from phi = 75% to phi = 33%, with one sensor located at X{\deg} = 3 cm, for the estimation of the advection coefficient. The OED has also been applied for the identification of couples of parameters. A sample submitted to multiple relative humidity steps (phi = 10-75-33-75%) with a sensor placed at X{\deg} = 5 cm was found as the best option for determining both properties with the same experiment. These OED parameters have then been used for the determination of moisture permeability and advection coefficients. The estimated moisture permeability coefficients are twice higher than the a priori values obtained using standard methods. The advection parameter corresponds to the mass average velocity of the order of v = 0.01 mm/s within the material and may play an important role on the simulation of moisture front., Comment: 34 pages, 14 figures, 6 tables, 43 references. Other author's papers can be downloaded at http://www.denys-dutykh.com/. arXiv admin note: text overlap with arXiv:1704.06565

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., Comment: 38 pages, 19 figures, 3 tables, 28 references. Other author's papers can be downloaded at http://www.denys-dutykh.com/

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 non-linear problems. To overcome this disadvantage, this paper explores the use of improved explicit schemes, such as Dufort-Frankel, Crank-Nicolson and hyperbolisation approaches. A first case study has been considered with the hypothesis of linear transfer. The Dufort-Frankel, Crank-Nicolson and hyperbolisation schemes were compared to the classical Euler explicit scheme and to a reference solution. Results have shown that the hyperbolisation scheme has a stability condition higher than the standard Courant-Friedrichs-Lewy (CFL) condition. The error of this schemes depends on the parameter \tau representing the hyperbolicity magnitude added into the equation. The Dufort-Frankel scheme has the advantages of being unconditionally stable and is preferable for non-linear transfer, which is the second case study. Results have shown the error is proportional to O(\Delta t). A modified Crank-Nicolson scheme has been proposed in order to avoid sub-iterations to treat the non-linearities 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 parallelise on high-performance computer systems. Although the approach is unconditionally stable, the choice of the time discretisation $\Delta t$ remains an important issue to accurately represent the physical phenomena., Comment: 35 pages, 16 figures, 1 table, 32 references. Other author's papers can be downloaded at http://www.denys-dutykh.com/. arXiv admin note: text overlap with arXiv:1612.07649

When comparing measurements to numerical simulations of moisture transfer through porous materials a rush of the experimental moisture front is commonly observed in several works shown in the literature, with transient models that consider only the diffusion process. Thus, to overcome the discrepancies between the experimental and the numerical models, this paper proposes to include the moisture advection transfer in the governing equation. To solve the advection-diffusion differential equation, it is first proposed two efficient numerical schemes and their efficiencies are investigated for both linear and nonlinear cases. The first scheme, Scharfetter-Gummel (SG), presents a Courant-Friedrichs-Lewy (CFL) condition but is more accurate and faster than the second scheme, the well-known Crank-Nicolson approach. Furthermore, the SG scheme has the advantages of being well-balanced and asymptotically preserved. Then, to conclude, results of the convective moisture transfer problem obtained with the SG numerical scheme are compared to experimental data from the literature. The inclusion of an advective term in the model may clearly lead to better results than purely diffusive models., Comment: 34 pages, 15 figures, 48 references. Other author's papers can be downloaded at http://www.denys-dutykh.com/

In the context of estimating material properties of porous walls based on in-site measurements and identification method, this paper presents the concept of Optimal Experiment Design (OED). It aims at searching the best experimental conditions in terms of quantity and position of sensors and boundary conditions imposed to the material. These optimal conditions ensure to provide the maximum accuracy of the identification method and thus the estimated parameters. The search of the OED is done by using the Fisher information matrix and a priori knowledge of the parameters. The methodology is applied for two case studies. The first one deals with purely conductive heat transfer. The concept of optimal experiment design is detailed and verified with 100 inverse problems for different experiment designs. The second case study combines a strong coupling between heat and moisture transfer through a porous building material. The methodology presented is based on a scientific formalism for efficient planning of experimental work that can be extended to the optimal design of experiments related to other problems in thermal and fluid sciences., Comment: 32 pages, 14 figures, 3 tables, 34 references. Other author's papers can be downloaded at http://www.denys-dutykh.com/