arXiv subjects

Julien Berger

Publications and source records attributed to Julien Berger.

29 records · Page 2Linked to original sources

arXiv2019

An adaptive simulation of nonlinear heat and moisture transfer as a boundary value problem

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.

cs.CE↗

arXiv2018

Advanced reduced-order models for moisture diffusion in porous media

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.

physics.comp-ph↗

arXiv2018

An efficient method to estimate sorption isotherm curve coefficients

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.

physics.app-ph↗

arXiv2018

On the solution of coupled heat and moisture transport in porous material

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.

physics.app-ph↗

arXiv2018

An improved explicit scheme for whole-building hygrothermal simulation

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.

cs.CE↗

arXiv2018

Solving nonlinear diffusive problems in buildings by means of a Spectral Reduced-Order Model

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.

physics.comp-ph↗

arXiv2018

Analysis and improvement of the VTT mold growth model: application to bamboo fiberboard

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.

math.OC↗

arXiv2018

Accurate numerical simulation of moisture front in porous material

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.

cs.CE↗

arXiv2017

On the estimation of moisture permeability and advection coefficients of a wood fibre material using the optimal experiment design approach

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° = 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° = 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.

math.OC↗

arXiv2017

Stable explicit schemes for simulation of nonlinear moisture transfer in porous materials

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 τrepresenting 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(Δt). 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 $Δt$ remains an important issue to accurately represent the physical phenomena.

cs.CE↗

arXiv2016

On the optimal experimental design for heat and moisture parameter estimation

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.

physics.comp-ph↗