arXiv subjects

Julien Berger

Publications and source records attributed to Julien Berger.

At least 19 recordsLinked to original sources

arXiv2025

Design and Experimental Validation of an Urban Microclimate Tool Integrating Indoor-Outdoor Detailed Longwave Radiative Fluxes at District Scale

Numerical simulation is a powerful tool for assessing the causes of an Urban Heat Island (UHI) effect or quantifying the impact of mitigation solutions on outdoor and indoor thermal comfort. For that purpose, several models have been developed at the district scale. At this scale, the outside surface energy budget is detailed, however building models are very simplified and considered as a boundary condition of the district scale model. This shortcoming inhibits the opportunity to investigate the effect of urban microclimate on the inside building conditions. The aim of this work is to improve the representation of the physical phenomena involved in the building models of a district model. For that purpose, the model integrates inside and outside fully detailed long-wave radiative flux. The numerical model is based on finite differences to solve conduction through all the surfaces and the radiosity method to solve long-wave radiative heat fluxes inside and outside. Calculated temperatures and heat fluxes are evaluated with respect to \textit{in situ} measurements from an experimental demonstrator over 14 sensors and a 24-day period. Results are also compared to state-of-the-art models simulation tool show improvement of the RMSE of $0.9 \ \mathsf{^{\,\circ}C}$ to $2.1 \ \mathsf{^{\,\circ}C}$ on the surface temperature modeled.

cs.CE↗

arXiv2025

Estimation of thermal properties and boundary heat transfer coefficient of the ground with a Bayesian technique

Urbanization is the key contributor for climate change. Increasing urbanization rate causes an urban heat island (UHI) effect, which strongly depends on the short- and long-wave radiation balance heat flux between the surfaces. In order to calculate accurately this heat flux, it is required to assess the surface temperature which depends on the knowledge of the thermal properties and the surface heat transfer coefficients in the heat transfer problem. The aim of this paper is to estimate the thermal properties of the ground and the time varying surface heat transfer coefficient by solving an inverse problem. The Dufort--Frankel scheme is applied for solving the unsteady heat transfer problem. For the inverse problem, a Markov chain Monte Carlo method is used to estimate the posterior probability density function of unknown parameters within the Bayesian framework of statistics, by applying the Metropolis-Hastings algorithm for random sample generation. Actual temperature measurements available at different ground depths were used for the solution of the inverse problem. Different time discretizations were examined for the transient heat transfer coefficient at the ground surface, which then involved different prior distributions. Results of different case studies show that the estimated values of the unknown parameters were in accordance with literature values. Moreover, with the present solution of the inverse problem the temperature residuals were smaller than those obtained by using literature values for the unknowns.

cs.CE↗

arXiv2022

Assessing the wall energy efficiency design under climate change using POD reduced order model

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.

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arXiv2022

Surface transfer coefficients estimation for heat conduction problem using the Bayesian framework

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.

cs.CE↗

arXiv2021

Average reduced model to simulate solutions for heat and mass transfer through porous material

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.

cs.CE↗

arXiv2021

An efficient sensitivity analysis for energy performance of a building envelope: a continuous derivative based approach

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.

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arXiv2021

Estimation of the thermal properties of an historic building wall by combining Modal Identification Method and Optimal Experiment Design

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.

cs.CE↗

arXiv2021

Searching an optimal experiment observation sequence to estimate the thermal properties of a multilayer wall under real climate conditions

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.

cs.CE↗

arXiv2021

Dimensionless formulation and similarity to assess the main phenomena of heat and mass transfer in building porous material

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.

cs.CE↗

arXiv2021

An efficient two-dimensional heat transfer model for building envelopes

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.

cs.CE↗

arXiv2021

Parametric PGD model used with orthogonal polynomials to assess efficiently the building's envelope thermal performance

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.

cs.CE↗

arXiv2021

Parameter estimation and model selection for water sorption in a wood fibre material

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.

stat.AP↗

arXiv2019

An efficient numerical method for a long-term simulation of heat and mass transfer: the case of an insulated rammed earth wall

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.

cs.CE↗

arXiv2019

On the comparison of three numerical methods applied to building simulation: finite-differences, RC circuit approximation and a spectral method

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.

cs.CE↗

arXiv2019

Evaluation of the reliability of building energy performance models for parameter estimation

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.

cs.CE↗

arXiv2019

A new model for simulating heat, air and moisture transport in porous building materials

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.

physics.app-ph↗

arXiv2019

An efficient numerical model for liquid water uptake in porous material and its parameter estimation

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.

cs.CE↗

arXiv2019

An innovative method to determine optimum insulation thickness based on non-uniform adaptive moving grid

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.

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