Julien Berger

Université Savoie Mont Blanc | UdS · LOCIE Optimization Laboratory of Design and Environmental Engineering

The estimation of wall thermal properties through an inverse problem procedure enables to increase the reliability of the model predictions for building energy efficiency. Nevertheless, it requires defining an experimental campaign to obtain in situ observations for existing buildings. The quality of the estimated parameter strongly depends on...

A d-optimum criterion is applied to the three-layer apparatus used for simultaneously estimating thermal properties (for example, thermal conductivity and effusivity) through the plane source method. The objective is to perform a comparison between uniform heating and piecewise-uniform heating of high-conductivity solid samples. In particular, the...

Current hygrothermal behaviour prediction models neglect the hysteresis phenomenon. This leads to a discrepancy between numerical and experimental results, and a miscalculation of buildings’ durability. In this paper, a new mathematical model of hysteresis is proposed and implemented in a hygrothermal model to reduce this discrepancy. The model is...

In this paper, the spectral method is developed as a reduced-order model for the solution of parametric problems within the building refurbishment framework. We propose to use the spectral reduced-order method to solve parametric problems in an innovative way, integrating the unknown parameter as one of the coordinates of the decomposition. The res...

Fault Detection and Diagnosis (FDD) is an important tool in building commissioning. Providing a consolidated dataset for FDD benchmarking is necessary to accurately evaluate the FDD prediction accuracy and detect anomalies. In this study, we provide an experimental dataset for an air handling unit containing two ducts linked by an air-to-air heat e...

Fault detection and diagnosis (FDD) are important tools to perform on-going monitoring of the systems and help in their building commissioning. An innovative method is investigated based on combined data-driven and knowledge-based approaches. This article presents the method. In the first phase, a so-called operating map of the system is built usin...

In the design context of Near-Zero Energy Buildings (nZEBs) and smart cities, robust and versatile optimization methods are needed to be coupled to simulation tools. In this way, the paper presents optimization algorithms coupled to a software with a capability to precisely simulate solar radiation availability by using a graphical pixel counting t...

For an experiment aimed at estimating thermal properties, the optimal experiment design is crucial in order to minimize the confidence region of the estimated parameters. To this end a D-optimum criterion requiring the maximization of the X^ T*X determinant (with X the sensitivity matrix), which in turn affects the covariance matrix of the estimate...

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 allow...

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...

In this article, both numerical and experimental investigations were carried out on the durability of hemp concrete. For this, an accelerated aging process was performed using cycles of immersion, freezing and drying. Then, an experimental campaign was enabled to determine heat and mass transfer properties, as well as the microstructure for both ag...

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 p...

Procédé d’analyse et procédé de détermination et de prédiction du régime de fonctionnement d’un système énergétique Un aspect de l’invention concerne procédé (100) d’analyse du régime de fonctionnement d’un système énergétique, le régime de fonctionnement du système énergétique étant caractérisé au moyen d’une pluralité de variables, dites variable...

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 Du Fort–Frankel approach that provides an explicit scheme with a relaxed stability condition. The model is first validated using an an...

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 Du Fort–Frankel approach that provides an explicit scheme with a relaxed stability condition. The model is first validated using an an...

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 p...

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...

The 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 ac...

Front Matter (Pages i-xviii) of the book: "Numerical Methods for Diffusion Phenomena in Building Physics: A Practical Introduction" by Nathan Mendes, Marx Chhay, Julien Berger and Denys Dutykh

Back Matter (Pages 233-245) of the book: "Numerical Methods for Diffusion Phenomena in Building Physics: A Practical Introduction" by Nathan Mendes, Marx Chhay, Julien Berger and Denys Dutykh

This article proposes an efficient explicit numerical model with a relaxed stability condition for the simulation of heat, air and moisture transfer in porous material. Three innovative approaches are combined to solve the system of two differential advection-diffusion equations coupled with a purely diffusive equation. First, the DuFort-Frankel sc...

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 integra...

This book is the second edition of Numerical methods for diffusion phenomena in building physics: a practical introduction originally published by PUCPRESS (2016). It intends to stimulate research in simulation of diffusion problems in building physics, by providing an overview of mathematical models and numerical techniques such as the finite diff...

Moisture is one of the main issues in building disorders. It can lead to microorganism's growth, material deterioration and impact on energy consumption. A comprehensive overview on the scale of the country considering climatic conditions may be an important starting point for potential moisture risks in building analyses. In this paper, we present...

In the field of building physics, diffusion phenomena started to be extensively modeled in the 70s (because of the oil crisis) to develop building-performance-simulation programs for the adoption of rational policies of energy conservation. However, existing tools might still present inconsistent scenarios of the actual occurrences in buildings, es...

This chapter is organized as follows. First, we present some theoretical bases behind spectral discretizations in Sect. 8.1. An application to a problem stemming from the building physics is given in Sect. 8.3. Finally, we give some indications for the further reading in Sect. 8.4. This document contains also a certain number of Appendices directly...

Above in Chap. 3 the basic finite differences approaches were presented. In particular, it was shown that explicit discretizations are subject to some additional constraints if one wants to have a stable numerical scheme. These restrictions are known in the literature under the name of Courant–Friedrichs–Lewy conditions [43]. For parabolic diffusio...

In building physics, as mentioned in Chaps. 2 and 3, numerical models used to predict heat and moisture transfer involve different characteristic time and lengths. Simulation of building behavior is generally analyzed on a time scale of 1 year (or more). However, the phenomena and particularly the boundary conditions evolve in seconds. The geometri...

This chapter is devoted to a practical presentation of the finite-element method (FEM). The focus is on the construction of numerical schemes rather than on the numerical properties that this approach benefits; References [5, 106] provide an introduction. A very large literature survey, sorted by fundamental references, mathematical foundations, ap...

Since the main focus of the Ph.D. school is set on the diffusion processes (molecular diffusion, heat and moisture conduction through the walls, etc.), it is desirable to explain how this research started and why the diffusion is generally modeled by parabolic PDEs [61]. The historic part of this chapter is partially based on [159].

In many engineering problems, including building modeling, the relevant information lies at the surface of a domain. In addition, only a few point-wise evaluations may be needed. Thus, classical numerical approaches would require a whole domain computation, which requires a considerable amount of information (and computation effort). The idea of us...

The first two parts of this book provided some theoretical background for solving diffusion problems in building physics and presented traditional (finite differences and finite elements) and nontraditional numerical methods (boundary integral approach, reduced order methods, and spectral methods). In addition, some practical examples were provided...

This chapter is entirely devoted to numerical methods, keeping in mind that the main application is on diffusion processes in building physics. However, the presentation is oriented to the practical construction of numerical schemes with an overview of their elementary numerical properties.

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 suff...

The building's energy consumption represents ca. 40% of the total energy consumption and ca. 20% of the CO2 emissions. With the improvement of new construction's efficiency the part of equipment's energy consumption increase more and more compared to the total building energy consumption. This article proposes to study a new approach in building's...

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 suff...

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 th...

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 th...

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...

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 th...

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...

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...

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 th...

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 o...

Prediction of moisture transfer within material using a classic diffusive model may lack accuracy, since numerical simulations underestimate the adsorption process when a sample is submitted to variations of moisture level. Model equations are always established with assumptions. Consequently, some phenomena are neglected. This paper therefore inve...

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...

Models for the prediction of heat and mass transfers in building porous materials have been developed since the 90’s with simulation programs such as MATCH, UMIDUS, DELPHIN and Wufi. These models are used to analyze the physical phenomena occurring and particularly the impact of moisture on buildings’ energy performance and durability. With this go...

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 provi...

Rising damp is one the main causes of moisture damages in historical buildings. The goal of this study is to propose an efficient numerical model for the predictions of capillary adsorption phenomena in porous material. The Scharfetter-Gummel numerical scheme is proposed to solve an advection-diffusion equation with gravity flux. Its advantages suc...

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 l...

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...

The standard methods to determine the vapour permeability and the moisture sorption curve may lack of accuracy since discrepancies are observed when comparing numerical predictions to experimental data. Moreover, these properties are determined in steady state conditions while the numerical predictions are carried in transient regime. Thus, this pa...

Comparisons of experimental observation of heat and moisture transfer through porous building materials with numerical results have been presented in numerous studies reported in the literature. However, some discrepancies have been observed, highlighting underestimation of sorption process and overestimation of desorption process. Some studies int...

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 mo...

This work is devoted to proposing a hybrid numerical–analytical method to address the problem of heat and moisture transfer in porous soils. Several numerical and analytical models have been used to study heat and moisture transfer. The complexity of the coupled transfer in soils is such that analytical solutions exist only for limited problems, wh...

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...

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 o...

This paper aims at estimating the sorption isotherm coefficients of a wood fiber material using experimental data. 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...

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 a...

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 neigh...

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 mod...

In this paper, an innovative method to minimise energy losses through building envelopes is presented, using the Proper Generalised Decomposition (PGD), written in terms of space x, time t, thermal diffusivity and envelope thickness L. The physical phenomenon is solved at once, contrarily to classical numerical methods that cannot create a paramete...

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...

Moisture is one of the main issues in building disorders. It can lead to microorganism's growth, discomfort, material deterioration and impact on energy consumption. In Brazil, there is a lack of assessment of the moisture risk potential in a comprehensive point of view, considering that most of the country is located in a tropical climate with imp...

This paper presents a review of the use of model reduction techniques for building physics applications. The use of separated representations, the so called Proper Generalised Decomposition (PGD), is particularly investigated. This technique can be applied for efficient building physics modelling at different levels: the wall and multizone models,...

In this paper, the use of Bayesian inference is explored for estimating both the thermal conductivity and the internal convective heat transfer coefficient of an old historic building wall. The room air temperature, as well as the temperatures at the surface and within the wall have been monitored during one year and then used to solve the identifi...

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 optima...

A proper generalised decomposition for solving inverse heat conduction problems is proposed in this article as an innovative method offering important numerical savings. It is based on the solution of a parametric problem, considering the unknown parameter as a coordinate of the problem. Then, considering this solution, all sets of cost function ca...

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 P...

Innovative and efficient ways to carry out numerical simulations are worth of investigation to reduce the computational complexity of building models and make it possible to solve complex problems. This paper presents a reduced order model, based on Proper Generalised Decomposition (PGD), to assess 2-dimensional heat and moisture transfer in walls....

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 d...

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 intere...

KEYWORDS: Model Order Reduction, HAM transfers, Proper Generalised Decomposition ABSTRACT: This paper proposes a reduced order model to simulate two-dimensional heat and moisture behaviour of material based on Proper General Decomposition (PGD). This innovative method is an a priori method. It proposes an alternative way for computing solutions of...

An excessive level of moisture in building damages their quality. Key factors associated to the development of this damages mainly depend on the hygrothermal fields inside building envelope. These key factors can be associated with HAM models to predict the development of moisture damages. Different granularities of HAM modelling exist in literatur...

This paper focuses on the issue of integrating two or three dimensional models of heat and moisture transfer in porous materials with whole building HAM modeling. To assess this aim, this paper proposes a reduced order model to simulate 2D Heat, air and moisture (HAM) behaviour in porous material. The reduction method used is the proper orthogonal...

In France, buildings represent 40% of the annual energy consumption. This sector represents an important stack to achieve the objective of reducing by 4 the greenhouse gas emissions by 2050. Knowledge of construction techniques and the use of equipments are the main keys to realize low energy buildings. To achieve this aim, we monitored 24 experime...