## No full-text available

To read the full-text of this research,

you can request a copy directly from the authors.

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.

To read the full-text of this research,

you can request a copy directly from the authors.

... Another adaptive method is the Quasi-Uniform Nonlinear Transformation (QUNT), which has been presented in An innovative method to determine optimum insulation thickness based on non-uniform adaptive moving grids (Gasparin et al., 2019b). The optimum insulation thickness of buildings walls is determined by taking into account the wall orientation and the position of the insulation in Brazilian buildings, which is determined through a parametric study. ...

... To illustrate the different applicabilities, Figure 4.1 presents some of the main criteria that can be used to evaluate the numerical methods: (i) spatial complexities, (ii) time scales and (iii) reduction of the computational cost. For example, if one aims at dealing with spatial complexities and accurate modelling of the phenomena at interfaces between two materials, the MOHL and QUNT are good candidates (Gasparin et al., 2018a(Gasparin et al., , 2019b. For coupling the model of heat and moisture transfer with others through co-simulation approaches (Wetter, 2011), the DuFort-Frankel is a very promising approach. ...

Building energy consumption is directly impacted by weather parameters such as temperature, solar radiation, atmospheric pressure, relative humidity and wind velocity. The knowledge of the building hygrothermal performance enables the design of energy efficient buildings and the prediction of overall durability and sustainability of envelopes. Therefore, designers and builders are interested in modeling the long-term performance of the envelopes by means of accurate, reliable and fast simulation tools.Several numerical models have been proposed in the literature to study the heat and moisture transfer in building materials. In general, this problem is solved by traditional methods, such as finite-difference and finite-volume methods, using mainly implicit schemes. Nevertheless, these methods impose costly sub-iterations to treat the nonlinearities and very fine discretization, which increase substantially the simulation computational cost. Therefore, this research has been focused on the development and analyses of numerical methods for efficiently simulate the problem of heat and mass transfer through porous materials.In the first part of this thesis, improved schemes of the traditional numerical methods have been developed to eliminate costly sub-iterations to treat nonlinearities, to improve the order of accuracy and to save computer run time. Despite the great progress with the new numerical schemes, the conclusion of the first part shows that we still have to deal with large systems of equations, particularly when treating multi-dimensional transfer problems. For this reason, to reduce even more the computational burden and the size of the system, a reduced-order model, based on spectral methods is proposed in the sequence to provide an accurate description of the physical phenomena. The degrees of freedom of the solution is strongly decreased while maintaining the model fidelity. It ensures a computational cost much lower than the complete original model.All these methods are applied to problems related to building physics, such as single and multilayer nonlinear transfer, the determination of optimum insulation thickness, the process of moisture buffer effects and transfer in one- or two-zone building models. In conclusion, we show how to build efficient numerical models, in terms of computational cost and accuracy, to investigate the heat and mass transfer in porous materials.

... The numerical models are used to solve the governing equation and assess the prediction of the physical phenomena are now described. In the literature, Eq. (3) can be solved using approaches such as finitedifference method [42], finite-volume method [6] or finite-element method [43]. For the sake of compactness, the finite-difference method is briefly presented as background of traditional approaches. ...

Within the environmental context, numerical modeling is a promising approach to assess the energy efficiency of building. Resilient buildings need to be designed, 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 usually. The model enables computing parametric solutions using basis interpolation on the tangent space of the Grassmann manifold. Three study cases are considered to verify the efficiency of the 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 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 optimum insulation thickness is calculated by analytical (Daouas 2011(Daouas , 2016 or numerical methods (Al-Sanea et al. 2005;Gasparin et al. 2019;Ozel 2019). Among the different numerical methods, several studies have used dynamic heat transfer model to calculate the heating and/or cooling transmission loads. ...

To improve the calculation accuracy of optimum insulation thickness of building walls, the effects of the initial conditions and the choice of the representative day used as boundary conditions on results have been studied. In this context, the unsteady heat transfer across the multilayer wall was considered as one-dimensional and the problem was solved numerically by an implicit finite difference method. A computational FORTRAN code has been developed and validated to calculate, under real meteorological data (RMD), the cooling transmission loads and the optimum insulation thickness during the summer period in the Sahara of Algeria. For steady periodic conditions, the influence of the initial conditions on the precision of the numerical result has been studied for two cases of representative days (July 15 and 21). By comparing the results with the case of real conditions (RMD), we find that the choice of July 15 as a typical day gives more accurate results than the choice of July 21. In addition, the difference of cooling transmission loads of 76.2% for July 15 and 76.31% for July 21 is observed, between the use of a repeated and another non-repeated typical day.

... This method was described independently in the seminal paper of Reference [38] and later in Reference [39]. Numerous subsequent developments were published in recent references [40][41][42]. The review of earlier works on the adaptive grid generation can be found in References [43,44]. ...

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

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.

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 important moisture sources. The current paper provides an overview on the potential risk of building moisture disorders, analysing the country differences of climate, population density, building standardization, type of construction methods and cultural issues. The main drawbacks reveal that many houses are built informally with lack of professional labor. Furthermore, the building standards do not consider the important moisture loads due to the climate and do not encourage the use of innovative techniques to deal with these issues. Climate, cultural and income differences within the country indicate there is a large potential for conducting research in Brazil on this topic with the perspectives of practical applications.

In Turkey the insulation of buildings was not a common occurrence until it became obligatory after the publication of the TS 825 Turkish Thermal Insulation Standard. However, most of the buildings still have little or no insulation. The aim of this study is to show the optimum insulation thicknesses for the different wall types; stone, brick and concrete, which are usually used in building construction in Turkey. Four cities from different climate zones, determined by the Turkish Thermal Insulation Standard (TS 825); Antalya (1st zone), İstanbul (2nd zone), Elazığ (3rd zone) and Kayseri (4th zone) were selected for analysis, and the optimum insulation thicknesses, energy savings and payback periods were calculated for each. Fiberglass, extruded polystyrene, expanded polystyrene and foamed polyurethane were the chosen insulation materials. The calculations were carried out with five different energy types; coal, LPG, electricity, fuel oil, and natural gas. As a consequence the results show that the optimum insulation thickness varies between 0.2cm and 18.6cm, energy savings vary between 0.038$/m2 and 250.415$/m2, and payback periods vary between 0.714 and 9.104years depending on the city, the type of wall, the insulation material and the cost of fuel.

We develop an adaptive method for solving one-dimensional systems of hyperbolic conservation laws, that employs a high resolution Godunov-type scheme for the physical equations, in conjunction with a moving mesh PDE governing the motion of the spatial grid points. Many other moving mesh methods developed to solve hyperbolic problems use a fully implicit discretization for the coupled solution-mesh equations, and so suuer from a signiicant degree of numerical stiiness. We employ a semi-implicit approach that couples the moving mesh equation to an eecient, explicit solver for the physical PDE, with the resulting scheme behaving in practice as a two-step predictor-corrector method. In comparison with computations on a xed, uniform mesh, our method exhibits more accurate resolution of discontinuities for a similar level of computational work.

In Tunisian climate, both heating in winter and cooling in summer are required to reach comfort levels. Due to the significant increase in building energy consumption, insulation of external walls is recently applied with a thickness typically ranging between 4 cm and 5 cm regardless of structure and orientation of walls and of economic parameters. In the present study, optimum insulation thickness, energy saving and payback period are calculated for a typical wall structure based on both cooling and heating loads. Yearly transmission loads are rigorously estimated using an analytical method based on Complex Finite Fourier Transform (CFFT). Considering different wall orientations, the west and east facing walls are the least favourite in the cooling season, whereas the north-facing wall is the least favourite in the heating season. A life-cycle cost analysis over a building lifetime of 30 years shows that the south orientation is the most economical with an optimum insulation thickness of 10.1 cm, 71.33% of energy savings and a payback period of 3.29 years. It is noted that wall orientation has a small effect on optimum insulation thickness, but a more significant effect on energy savings which reach a maximum value of 23.78 TND/m2 in the case of east facing wall. A sensitivity analysis shows that economic parameters, such as insulation cost, energy cost, inflation and discount rates and building lifetime, have a noticeable effect on optimum insulation and energy savings. Comparison of the present study with the degree-days model is also performed.

In the last decade, several numerical techniques have been developed to solve time-dependent partial differential equations (PDEs) in one dimension having solutions with steep gradients in space and in time. One of these techniques, a moving-grid method based on a Lagrangian description of the PDE and a smoothed-equidistribution principle to define the grid positions at each time level, has been coupled with a spatial discretization method that automatically discreizes the spatial part of the user-defined PDE following the method of lines approach. We supply two FORTRAN subroutines, CWRESU and CWRESX, which compute the residuals of the differential algebraic equations (DAE) system obtained from semidiscretizing, respectively, the PDE and the set of moving-grid equations. These routines are combined in an enveloping routine SKMRES, which delivers the residuals of the complete DAE system. To solve this stiff, nonlinear DAE system, a robust and efficient time-integrator must be applied, for example, a BDF method such as implemented in the DAE solvers SPRINT [Berzins and Furzeland 1985; 1986; Berzins et al. 1989] and DASSL [Brenan et al. 1989; Petzold 1983]. Some numerical examples are shown to illustrate the simple and effective use of this software interface.

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 difference and finite-element methods traditionally used in building simulation tools. Nonconventional methods such as reduced order models, boundary integral approaches and spectral methods are presented, which might be considered in the next generation of building-energy-simulation tools. In this reviewed edition, an innovative way to simulate energy and hydrothermal performance are presented, bringing some light on innovative approaches in the field.

The acronym HVAC&R stands for heating, ventilating, air-conditioning, and refrigerating. The combination of these processes is equivalent to the functions performed by air-conditioning. Because I-P units are widely used in the HVAC&R industry in the U.S., I-P units are used in this chapter.

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

The existing stock of buildings is a major contributor to energy-related carbon emissions. Significant savings in building energy consumption can be derived through retrofit. Building retrofits are typically guided by analyses through building energy simulation models. Due to the complexity of the physical characteristics of building systems and the lack of field measured data, modellers very often have to work with unknown or unmeasurable parameters either through approximation or with reference to the original design values. Since the values of these parameters usually fail to accurately represent the current conditions of existing buildings, it is important to calibrate these parameters before applying them in a building energy simulation model. In addition, it is also important to rank the input parameters according to their influence on building energy performance when identifying priorities for building retrofit. In this paper, a metamodel-based Bayesian method is proposed to simultaneously calibrate and rank input parameters to building energy simulation models. This proposed method implements both a model calibration procedure and parameter ranking procedure simultaneously when performing an analysis, which is much more efficient than applying these two procedures individually in separate model runs. As a further contribution, we extend the proposed method to one capable of handling large datasets. A case study is developed to demonstrate the accuracy and efficiency of the proposed method. Findings from the case study show that the calibrated parameters are usually different from the initially assumed values. In the context of the chosen existing building in Singapore, most of the considered parameters are key factors influencing building energy performance with cooling plant COP being the most important factor and natural exfiltration rate being the least important factor.

A simultaneous calibration and parameter ranking method is developed. • This method is accurate and computationally efficient compared to others. • This method can help derive more reliable inputs for building energy modellers. • This method can help identify priorities in retrofit for energy efficient buildings. A B S T R A C T The existing stock of buildings is a major contributor to energy-related carbon emissions. Significant savings in building energy consumption can be derived through retrofit. Building retrofits are typically guided by analyses through building energy simulation models. Due to the complexity of the physical characteristics of building systems and the lack of field measured data, modellers very often have to work with unknown or unmeasurable parameters either through approximation or with reference to the original design values. Since the values of these parameters usually fail to accurately represent the current conditions of existing buildings, it is important to calibrate these parameters before applying them in a building energy simulation model. In addition, it is also important to rank the input parameters according to their influence on building energy performance when identifying priorities for building retrofit. In this paper, a metamodel-based Bayesian method is proposed to simultaneously calibrate and rank input parameters to building energy simulation models. This proposed method implements both a model calibration procedure and parameter ranking procedure simultaneously when performing an analysis, which is much more efficient than applying these two procedures individually in separate model runs. As a further contribution, we extend the proposed method to one capable of handling large datasets. A case study is developed to demonstrate the accuracy and efficiency of the proposed method. Findings from the case study show that the calibrated parameters are usually different from the initially assumed values. In the context of the chosen existing building in Singapore, most of the considered parameters are key factors influencing building energy performance with cooling plant COP being the most important factor and natural ex-filtration rate being the least important factor.

Several studies have shown that the actual thermal performance of buildings after construction may deviate significantly from its performance anticipated at design stage. As a result, there is growing interest in on site testing as a means to assess real performance. The IEA EBC Annex 58-project ‘Reliable Building Energy Performance Characterisation Based on Full Scale Dynamic Measurements’ focused on on site testing and dynamic data analysis methods that can be used to characterise the actual thermal performance and energy efficiency of building components and whole buildings. The research within this project was driven by case studies. The current paper describes one of them: the thermal characterisation of a round robin test box. This test box can be seen as a scale model of a building, and was built by one of the participants. During the project, its fabric properties remained unknown to all other participants. Full scale measurements have been performed on the test box in different countries under real climatic conditions. The obtained dynamic data has been distributed to all participants who had to characterise the thermal performance of the test box’s fabric based on the provided data. The paper compares the result of different techniques, ranging from a simple quasi-stationary analysis to advanced dynamic data analysis methods, which can be used to characterise the thermal performance based on on-site collected data.

h i g h l i g h t s The transient energy ratio and effective U-value are defined. Energy consumption during intermittent occupancy is very different from that predicted by static analyses. In cold climates, high thermal mass structures will often use more energy than low thermal mass structures. Current assumptions regarding the energy savings of high thermal mass structures may often be flawed. a b s t r a c t This paper presents new metrics to measure the effect of thermal mass on the energy required to heat and cool buildings. Previous studies have been flawed as they have not considered the interaction between intermittent occupancy and thermal mass, which has a significant impact on overall energy use. However, existing parameters do not adequately capture these effects, so the new metrics developed in this paper are used to analyse the impact of thermal mass in hot climates with active cooling, and cold climates with active heating. The results agree with existing literature that high thermal mass structures are likely to be effective in hot climates; however, in cold climates the drawbacks of high thermal mass likely outweigh the advantages, and high thermal mass can cause an increase in energy use. This finding has implications for the design of buildings in cold climates, and contradicts the commonly-held assumption that high thermal mass is correlated with low energy use. The new metrics (transient energy ratio and effective U-value) provide a generalisable method to quantify these effects. They are further used here to analyse the dynamic performance of heavily insulated buildings and show that high thermal mass often leads to higher energy use in cold climates.

The thermal behaviour of buildings in transient conditions is established by the temperature evolution of the external environment. Determining the thermal evolution of buildings is of crucial importance for building energy design, as well as for energetic performance evaluation. Building energy performance evaluation and calculation of energy use for space heating and cooling can be carried out by several methods of various degrees of complexity and accuracy. These methods are implemented in such simulation codes as NBLSD, Il DOE-II, ENERGY PLUS and others. In order to comply with the Energy Performance of Buildings Directive (EPBD), the studies and research in this field start from the Directive 91/2002/CE and subsequently lead to the EN ISO 13790:2007. The latter proposes a thermal model for a building composed of five resistances and one capacity, called R5C1, and also offers its dynamic solution with a simple hourly computational model. The present paper suggests the solution and dynamic simulation of the R5C1 model and an evaluation of its use in building energy design. Finally, a case study regarding a typical average day in June in Catania (Sicily, Italy) is presented. The implemented model and the relative simulation results have confirmed the advantages of such a solution and have been validated for some modules of the CONPHOEBUS scrl Research Building in Catania. The proposed model has the advantage of a small number of parameters (5 thermal resistances and 1 thermal capacity) and has a simple formulation and then requires low computational resources. Furthermore, this model allows the correct estimation of the user profile with few and not sufficiently precise input data. Due to the above listed properties the proposed model was adopted by the Italian National Agency for New Technologies, Energy and Sustainable Economic Development (ENEA) for an extensive energy consumption simulation campaign involving 5000 buildings in Italy (a campaign of measurements on 20,000 buildings planned for 2017) for the calculation of statistical consumption data for public buildings.

The increase outdoor temperature acts directly on the indoor climate of buildings. In Cameroon, the energy consumption demand in the buildings sector has been rapidly increasing in recent years; so well that energy supply does not always satisfy demand. Thermal insulation technology can be one of the leading method for reducing energy consumption in these new buildings. However, choosing the thickness of the insulation material often causes high insulation costs. In the present study, the optimum insulation thickness, energy saving and payback period were calculated for buildings in Yaoundé and Garoua cities, located in two climate regions in Cameroon.The economic model including the cost of insulation material and the present value of energy consumption and the cost over a life time of 22 years of the building, were used to find the optimum insulation thickness,energy saving, and payback period. Materials that extruded polystyrene were chosen and used for two typical wall structures (Concrete block(HCB) and compressed stabilized earth block wall (CSEB)).They early cooling transmission loads, according to wall orientations and percentage of radiation blocked were calculated using the explicit finite-difference method under steady periodic conditions. As a result, it was found that the west- and east-facing walls are the least favourite in the cooling season, whereas the south and north orientations are the most economical. Although wall orientation had a significant effect on the optimum insulation thickness, it had a more significant effect on energy savings. In equatorial region(Yaoundé), for south orientation, the optimum insulation thickness was 0.08 m for an energy savings of 51.69 $/m2. Meanwhile, in tropical region(Garoua), for north orientation, the optimum insulation thickness was 0.11 m for an energy savings of 97.82 $/m2.

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 parameter dependent model. First, the PGD solution is validated with an analytical solution to prove its accuracy. Then a complex case study of a multi-layer wall submitted to transient boundary conditions is investigated. The parametric solution is computed as a function of the space and time coordinates, as well as the thermal insulation thickness and the load material thermal diffusivity. Physical behaviour and conduction loads are analysed for 76 values of thermal insulation thickness and 100 types of load material properties. Furthermore, the reduced computational cost of the PGD is highlighted. The method computes the solution 100 times faster than standard numerical approaches. In addition, the PGD solution has a low storage cost, providing interesting development of parametric solutions for real-time applications of energy management in buildings.

Implicit schemes have been extensively used in building physics to compute the solution of moisture diffusion problems in porous materials for improving stability conditions. Nevertheless, these schemes require important sub-iterations when treating nonlinear problems. To overcome this disadvantage, this paper explores the use of improved explicit schemes, such as Dufort–Frankel, Crank–Nicolson and hyperbolization approaches. A first case study has been considered with the hypothesis of linear transfer. The Dufort–Frankel, Crank–Nicolson and hyperbolization schemes were compared to the classical Euler explicit scheme and to a reference solution. Results have shown that the hyperbolization scheme has a stability condition higher than the standard Courant–Friedrichs–Lewy condition. The error of this schemes depends on the parameter τ representing the hyperbolicity magnitude added into the equation. The Dufort–Frankel scheme has the advantages of being unconditionally stable and is preferable for nonlinear transfer, which is the three others cases studies. Results have shown the error is proportional to O(dt). A modified Crank–Nicolson scheme has been also studied in order to avoid sub-iterations to treat the nonlinearities at each time step. The main advantages of the Dufort–Frankel scheme are (i) to be twice faster than the Crank–Nicolson approach; (ii) to compute explicitly the solution at each time step; (iii) to be unconditionally stable and (iv) easier to parallelize on high-performance computer systems. Although the approach is unconditionally stable, the choice of the time discretization remains an important issue to accurately represent the physical phenomena.

This paper investigates the impact of moisture content on the thermal inertia parameters of building material layers. Moisture variation affects the energy storage and therefore the energy gains/losses through buildings. To this effect the decrement factor and time lag are determined for three types of concrete layers and one of solid clay-bricks masonry layer. Their consideration is essential to enhance the design of building elements, from a thermal point of view, when exposed to varying moisture content conditions. Moisture content and relative humidity variations of each analysed layer, as defined by specific moisture storage functions, are shown to interrelate non-linearly with the layer resistor–capacitor circuit section parameters (thermal conductivity and volumetric heat capacity) showing notable consequences on the thermal inertia parameters. The dynamic thermal analysis is accomplished by using the thermal-circuit modelling approach and the nodal solution method. The deterioration of decrement factor and time lag due to moisture content are illustrated by appropriate metrics. Computer results for the studied layers with thicknesses varying from 10 cm to 50 cm show the influence of the variation of relative humidity and thickness on the decrement factor and time lag.

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

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

Abstract Experimental identification of the dynamic models of heat transfer in walls is needed for optimal control and characterization of building energy performance. These models use the heat equation in time domain which can be put in matrix form and then, through state-space representation, transformed in a transfer function which is of infinite order. However, the model acts as a low-pass filter and needs to respond only to the frequency spectrum present in the measured inputs. Then, the order of the transfer function can be determined by using the frequency spectrum of the measured inputs and the accuracy of the sensors. The main idea is that from two models of different orders, the one with a lower order can be used in building parameter identification, when the difference between the outputs is negligible or lower than the output measurement error. A homogeneous light wall is used as an example for a detailed study and examples of homogeneous building elements with very high and very low time constants are given. The first order model is compared with a very high order model (hundreds of states) which can be considered almost continuous in space.

This research work deals with an Environmental Research Institute (ERI) building where an underfloor heating system and natural ventilation are the main systems used to maintain comfort condition throughout 80% of the building areas. Firstly, this work involved developing a 3D model relating to building architecture, occupancy & HVAC operation. Secondly, the calibration methodology, which consists of two levels, was then applied in order to insure accuracy and reduce the likelihood of errors. To further improve the accuracy of calibration a historical weather data file related to year 2011, was created from the on-site local weather station of ERI building. After applying the second level of calibration process, the values of Mean bias Error (MBE) and Cumulative Variation of Root Mean Squared Error (CV(RMSE)) on hourly based analysis for heat pump electricity consumption varied within the following ranges: (MBE)hourly from −5.6% to 7.5% and CV(RMSE)hourly from 7.3% to 25.1%. Finally, the building was simulated with EnergyPlus to identify further possibilities of energy savings supplied by a water to water heat pump to underfloor heating system. It found that electricity consumption savings from the heat pump can vary between 20% and 27% on monthly bases.

Building energy use represents approximately 25% of the average total global energy consumption (for both residential and commercial buildings). Heating, ventilation, and air conditioning (HVAC) – in most climates – embodies the single largest draw inside our buildings. In many countries around the world a concerted effort is being made towards retrofitting existing buildings to improve energy efficiency. Better windows, insulation, and ducting can make drastic differences in the energy consumption of a building HVAC system. Even with these improvements, HVAC systems are still required to compensate for daily and seasonal temperature swings of the surrounding environment. Thermal mass inside the thermal envelope can help to alleviate these swings. While it is possible to add specialty thermal mass products to buildings for this purpose, commercial uptake of these products is low. Common building interior building materials (e.g. flooring, walls, countertops) are often overlooked as thermal mass products, but herein we propose and analyze non-dimensional metrics for the ‘benefit’ of selected commonly available products. It was found that location-specific variables (climate, electricity price, material price, insolation) can have more than an order of magnitude influence in the calculated metrics for the same building material. Overall, this paper provides guidance on the most significant contributors to indoor thermal mass, and presents a builder- and consumer-friendly metric to inform decisions about which products could best improve the thermal behavior of the structure.

This paper aims to focus on the comparison of the building energy performance assessment between ANSI/ASHRAE Standard 90.1—2007 and the Regulation for Energy Efficiency Labeling of Buildings in Brazil. A computational simulation using the EnergyPlus program has been conducted to evaluate the energy ratings of commercial and residential buildings located in three cities in Brazil: Brasília, Rio de Janeiro and Belém. The building energy ratings were determined based on the Regulation for Energy Efficiency Labeling of Commercial Buildings in Brazil, the Regulation for Energy Efficiency Labeling of Residential Buildings in Brazil and the ANSI/ASHRAE Standard 90.1—2007. The results for the commercial buildings show that there is equivalence between levels A to C of the Brazilian regulation and the reference model from ANSI/ASHRAE Standard 90.1—2007, depending on the climate adopted. For residential buildings, the reference model from ANSI/ASHRAE Standard 90.1—2007 resulted in higher energy consumption than level C from the Brazilian regulation for all the climates analyzed. Meanwhile, the buildings energy ratings based on the Brazilian regulation were also compared with the minimum energy performance required for Leadership in Energy and Environmental Design.

Thermal insulation is generally installed in the envelope of residential buildings to improve their thermal performance. However, the selection of the optimum insulation thickness requires a detailed thermal energy and economic analysis. This paper determines the optimum insulation thickness for external walls of different composition and orientation, considering both the heating and cooling period and taking into account the wind speed and direction. Three types of composite, thermally insulated walls have been selected. Annual heating and cooling transmission loads are being calculated based on transient heat flow through the external walls and by using hourly climatic data of the city of Athens, Greece. The available wind speed and direction data have been statistically analyzed for the assessment of the prevalent wind directions in the area. An economic analysis, based on the life cycle savings method has been performed for each configuration, various thicknesses of insulation material and different orientations. The optimum insulation thickness for any type of wall and orientation was found to be between 7.1 cm and 10.1 cm. Furthermore, a sensitivity analysis indicates whether changes of the economic parameters affect the optimum insulation thickness.

Mortar joints which cut across insulation layers in building walls act as thermal bridges that increase transmission loads and reduce wall thermal resistance (R-value). A computer model based on the finite-volume method, which has been previously validated, is used to quantify effects of mortar joints height (Hmj) on thermal performance of building walls under two-dimensional steady-periodic conditions using the climatic data of Riyadh. Results show that for a typical wall with insulation thickness of 75 mm, mortar joints with Hmj = 10 mm (4.8% thermal bridge area) increase peak, daily, and yearly cooling and heating transmission loads by 62%, while the wall R-value decreases by 38% compared to similar wall with no mortar joints (Hmj = 0). The transmissions loads increase by 103% and the R-value decreases by 51% for Hmj = 20 mm (9.1% thermal bridge area). These percentages would drastically increase building air-conditioning loads and energy consumption. Thermal bridges are also shown to appreciably increase the decrement factor causing higher inner surface temperature and transmission load fluctuations. It is strongly recommended that thermal bridging effects should be minimized, if not eliminated, through proper design practices and that, when unavoidably present, must be given due consideration in thermal analysis and must be accounted for.

In this study the variations of concrete density and concrete thermal conductivity of various wall assemblies are considered to analyse their influence on the dynamic thermal characteristics, such as the decrement factor and time lag. The assemblies under study refer to insulated walls with variable concrete density and the concrete placement in one or two layers. The insulation is also placed as one or two equivalent layers giving rise to a total of six typical wall configurations. The thermal inertia parameters are determined using the thermal-circuit modelling approach and the analysis is based on the nodal solution method. Density and conductivity variations of the concrete layers are seen to interrelate non-linearly with the walls’ RC-sections corresponding parameters with consequences on its inertia parameters. As such variations, together with the studied insulation placements, affect the decrement factor and time lag in a different fashion, metrics for assessing the walls’ thermal behaviour from a proportional (PDM, PTM) and a relative (RDM, RTM) point of view are introduced. Computer results, showing the impact of the variations of concrete density and conductivity on the decrement factor, time lag and the proposed metrics are presented for all the studied wall assemblies.
Keywords: Thermal circuit model; Transient analysis; Concrete density/conductivity; Decrement factor; Time lag

The “Solar Complex of Plan-les-Ouates” is a traditional multifamily building with some commercial and administrative areas. It was designed to consume a minimum amount of thermal energy by combining several renewable energy systems (1400m2 of solar roof, buried pipe and exhausted air heat exchangers) with an optimised envelope and electrical equipment. Initially predicted to consume 160MJ/m2 per year of gas, a gas energy use index (per unit heated floor area) of 246MJ/m2 per year was measured. The energy analysis of the building, based on a 3-year period of monitoring, brought up the most relevant points that explain this difference: the real conditions of utilisation (such as the interior temperature) and the real performance of the complete technical system are not taken into account in the theoretical value. Both technical and economical aspects of the renewable energy systems were analysed in detail. An important lesson learned from this experiment is that the energy concept of buildings must be simple and consistent and the complexity of the technical installations must be carefully managed from the design-stage to the exploitation. Detailed monitoring of innovative low-energy buildings is recommended to understand the possible discrepancies between theoretical and real heat consumption and to improve the transfer of new energy technologies to large-scale real constructions.

The modeling of the thermal behavior of buildings requires using relatively heavy data processing when it comes to reproducing reality accurately. Electrical analogy makes it possible to develop directly accurate and simplified models insofar as the temperatures within the walls are not required.We present the various stages, which led us to propose the global analogical model of the building. Initially, we have studied how to transform a multi-layer wall into a three resistances and four capacities model (3R4C). We will compare this model with other electrical models thanks to a time and frequency analysis. Then, we will deal with the principle of aggregation of several walls. In order to facilitate the iterative resolutions related to numerical simulations, the lumped model integrates a heating floor.

A comprehensive economic analysis has been performed to inter-relate the optimum thickness of insulation materials for various wall orientations. The yearly cooling and heating transmission loads of building walls were determined by use of implicit finite-difference method with regarding steady periodic conditions under the climatic conditions of ElazIg, Turkey. The economic model including the cost of insulation material and the present value of energy consumption cost over lifetime of 10Â years of the building was used to find out the optimum insulation thickness, energy savings and payback periods for all wall orientations. Considered insulation materials in the analysis were extruded polystyrene and polyurethane. As a result, the optimum insulation thickness of extruded polystyrene was found to be 5.5Â cm for south oriented wall and 6Â cm for north, east and west oriented walls. Additionally, the lowest value of the optimum insulation thickness and energy savings were obtained for the south oriented wall while payback period was almost same for all orientations.

Due to the lack of a building simulation program that can simulate in details the combined heat, vapor, and liquid transfer
in porous elements and the HVAC (heating, ventilation and air-conditioning) systems, a flexible computational algorithm has
been elaborated in order to integrate models for both HVAC systems and multizone hygrothermal building model. In the algorithm,
models for the primary system-composed of chiller, cooling tower, primary pumps, and condensation pumps—have been described.
For the secondary system, models for the cooling and dehumidifying coil, humidifier, fan, and mixing box have been considered.
Those mathematical models have been integrated into the whole-building PowerDomus simulation environment. The simulation environment
is presented, and results show the usability aspects of the proposed computer environment by comparing air- and water-cooled
equipment.

Thermal insulation is one of the most effective energy-conservation measures in buildings. Despite the widespread use of insulation materials in recent years, little is known regarding their optimum thickness under dynamic thermal conditions. Insulated concrete blocks are among the units most commonly used in the construction of building walls in Saudi Arabia. Typically, the insulation layer thickness is fixed at a value in the range 2.5–7.5 cm, regardless of the climatic conditions, type and cost of insulation material, and other economic parameters. In the present study, a numerical model based on a finite-volume, time-dependent implicit procedure, which has been previously validated, is used to compute the yearly cooling and heating transmission loads under steady periodic conditions through a typical building wall, for different insulation thicknesses. The transmission loads, calculated by using the climatic conditions of Riyadh for a west-facing wall, are fed into an economic model in order to determine the optimum thickness of insulation (Lopt). The latter corresponds to the minimum total cost, which includes the cost of insulation material and its installation plus the present value of energy consumption cost over the lifetime of the building. The optimum insulation thickness depends on the electricity tariff as well as the cost of insulation material, lifetime of the building, inflation and discount rates, and coefficient of performance of the air-conditioning equipment. In the present study, the effect of electricity tariff on the computed optimum insulation thickness is investigated. Different average electricity tariffs are considered; namely, 0.05, 0.1, 0.2, 0.3 and 0.4 SR/kWh (designated as Cases 1–5, respectively; 1 US$ = 3.75 Saudi Riyals). Results using moulded polystyrene as an insulating material show that the values of Lopt are: 4.8, 7.2, 10.9, 13.7 and 16.0 cm for Cases 1–5. Under the conditions of optimal insulation thickness for each electricity tariff, Case 1 gives the lowest total cost of 17.4 SR/m2, while Case 5 gives the highest total cost of 53.1 SR/m2. Corresponding thermal performance characteristics in terms of yearly total and peak transmission loads, R-value, time lag and decrement factor are presented.

Energy conscious building design consists in controlling the thermophysical characteristics of the building envelope such as, firstly, thermal transmittance (U-value). However, besides the U-value, the envelope thermal inertia should also be considered. The literature studies report very different estimations regarding the energy saving potential associated with the use of an adequate inertia, ranging from a few percentages to more than 80%. Therefore, this study aims at assessing the parameters enhancing or damping the role of thermal inertia, providing a variety of results. For this purpose several external wall systems with the same U-value but different dynamic properties were investigated to calculate the associated achievable energy savings. A parametric analysis was performed in progressive steps, by running the models of a virtual Test Cell and of a sample building. Both design parameters (heat transfer surface, solar control) and operational ones (ventilation rates, HVAC functional regime) were varied.It was found that the highest energy performance wall system has a proper combination of the dynamic thermal transmittance and thermal admittance values, although not necessarily the best ones. Moreover, it was shown that thermal inertia effects are enhanced if it is coupled with other energy saving measures and an efficient building use.

Association of Refrigeration, Air Conditioning, Ventilation and Heating

- Abrava Brazilian

ABRAVA. Brazilian Association of Refrigeration, Air Conditioning, Ventilation and Heating,
2019. 4

Brazilian Energy Balance

- F C Filho

F. C. Filho. Brazilian Energy Balance. Technical report, Ministry of Mines and Energy -MME, Brasilia, 2017. 4

A metric for characterizing the effectiveness of thermal mass in building materials

- R A Taylor
- M Miner

Taylor RA, Miner M (2014) A metric for characterizing the
effectiveness of thermal mass in building materials. Appl Energy
128(Supplement C):156-163

E-mail address: Denys.Dutykh@univ-smb

- France Chambéry
- Lama Cnrs
- Université Savoie Mont
- Blanc

Chambéry, France and LAMA, UMR 5127 CNRS, Université Savoie Mont Blanc, Campus
Scientifique, F-73376 Le Bourget-du-Lac Cedex, France
E-mail address: Denys.Dutykh@univ-smb.fr
URL: http://www.denys-dutykh.com/
N. Mendes: Thermal Systems Laboratory, Mechanical Engineering Graduate Program, Pontifical Catholic University of Paraná, Rua Imaculada Conceição, 1155, CEP:
80215-901, Curitiba -Paraná, Brazil
E-mail address: Nathan.Mendes@pucpr.edu.br
URL: https://www.researchgate.net/profile/Nathan_Mendes/

International Energy Agency energy conservation in buildings and community systems programme. Heat, air and moisture transfer through new and retrofitted insulated envelope parts: [IEA] (Hamtie); Annex 24 Task 3/Final report: Material properties. Laboratorium Bouwfysica

- M K Kumaran

Kumaran MK (1996) International Energy Agency energy conservation in buildings and community systems programme. Heat,
air and moisture transfer through new and retrofitted insulated
envelope parts: [IEA] (Hamtie);

Thermal transients simulations of a building by a dynamic model based on thermal-electrical analogy: evaluation and implementation issue

- N Mendes
- M Chhay
- J Berger
- D Dutykh

Mendes N, Chhay M, Berger J, Dutykh D (2016) Numerical
methods for diffusion phenomena in building physics. PUC Press,
Curitiba
16. Capizzi G, Sciuto GL, Cammarata G, Cammarata M (2017)
Thermal transients simulations of a building by a dynamic
model based on thermal-electrical analogy: evaluation and
implementation issue. Appl Energy 199:323-334

Standard 90.1-2013: energy standard for buildings except low-rise residential buildings

ASHRAE (2013) Standard 90.1-2013: energy standard for buildings except low-rise residential buildings. I-P edition

Brazilian Association of Technical Standards, NBR 15220: Desempenho térmico de edificações

ABNT (2005) Brazilian Association of Technical Standards, NBR
15220: Desempenho térmico de edificações

Numerical solution of conservation laws on moving grids

- G S Khakimzyanov
- D Dutykh
- D E Mitsotakis
- N Y Shokina

G. S. Khakimzyanov, D. Dutykh, D. E. Mitsotakis, and N. Y. Shokina. Numerical solution
of conservation laws on moving grids. Submitted, pages 1-28, 2018. 5, 6, 7, 9, 10, 11

address: suelengasparin@hotmail

- S Gasparin

S. Gasparin: LAMA, UMR 5127 CNRS, Université Savoie Mont Blanc, Campus Scientifique, F-73376 Le Bourget-du-Lac Cedex, France and Thermal Systems Laboratory,
Mechanical Engineering Graduate Program, Pontifical Catholic University of Paraná,
Rua Imaculada Conceição, 1155, CEP: 80215-901, Curitiba -Paraná, Brazil
E-mail address: suelengasparin@hotmail.com
URL: https://www.researchgate.net/profile/Suelen_Gasparin/
J. Berger: LOCIE, UMR 5271 CNRS, Université Savoie Mont Blanc, Campus Scientifique, F-73376 Le Bourget-du-Lac Cedex, France
E-mail address: Berger.Julien@univ-smb.fr
URL: https://www.researchgate.net/profile/Julien_Berger3/