Nathan Mendes

• PhD
• Managing Director at Pontifical Catholic University of Paraná

Solar energy utilization in buildings can significantly contribute to energy savings and enhance on-site energy production. However, excessive solar gains may lead to overheating, thereby increasing cooling demands. Accurate calculation of sunlit and shaded areas is essential for optimizing solar technologies and improving the precision of building...

This study presents an approach to simulating building-integrated photovoltaic glazing systems composed of semitransparent organic photovoltaic (ST-OPV) elements. The approach consists of a mathematical cosimulation model based on the energy balance of complex glazing systems, considering heat transfer as conduction, mixed convection, and radiation...

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

Summer mortality of Crassostrea gigas occurs in Brazilian crops, with predominance in the final phase of cultivation, when they reach the commercial size, generating significant losses for local producers. In order to mitigate this problem, a technical solution, whose principle is based on long-term confinement at low temperatures (10 −12°C) for in...

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

The phenomenon of summer mortality in Pacifi c oysters cultures also occurs in Brazilian crops, with predominance in the adult phase, generating signifi cant losses for local producers. In the search for a technological solution to mitigate its effects, the mechanical vapour compression and hydraulic refrigeration concepts are evaluated as two prop...

A two-dimensional model is proposed for energy efficiency assessment through the simulation of heat transfer in building envelopes, considering the influence of the surrounding environment. The model is based on the Du Fort–Frankel approach that provides an explicit scheme with a relaxed stability condition. The model is first validated using an an...

A two-dimensional model is proposed for energy efficiency assessment through the simulation of heat transfer in building envelopes, considering the influence of the surrounding environment. The model is based on the Du Fort–Frankel approach that provides an explicit scheme with a relaxed stability condition. The model is first validated using an an...

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

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

Multi-criteria design techniques applied to the analysis of shading devices of buildings have arisen as useful tools for architects. Even though several techniques have been applied to shading devices with simple geometries, they usually require numerous simulations to suitably complete the analysis, making the optimization process time-consuming....

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

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

Building Energy Simulation (BES) tools commonly use 1-D formulation for computing conductions loads through building envelopes. As this assumption may cause significant errors on the prediction of building energy and thermal performance, this work proposes a methodology for taking into account the 3-D heat transfer phenomenon nature and compare the...

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

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

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

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

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

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

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

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

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

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

Thermal comfort conditions may vary substantially within an air-conditioned room equipped by split-type systems. In this work, the comfort conditions in a classroom were evaluated experimentally based on the PMV index, according to ISO 7730 Standard that defines the thermal satisfaction in occupied environments. The experiment was carried out at th...

In this paper, the results of the validation modeling of glazing systems and an application based on Semi-transparent organic photovoltaics (ST-OPVs) are re-ported. A numerical code was developed for research purposes to improve the glazing modeling in building energy performance taking into account spectral radiative properties in glazing, buildin...

A new Building and Environment Simulation Platform (BESP) has been conceived to be an advanced multidimensional simulation platform for fast and accurate assessment of energy and hygrothermal performance of building elements, buildings and building communities by means of an intelligent co-simulation approach among building energy simulation tools...

A precise hygrothermal model is essential to predict the energy performance of building envelopes providing coupled transport of mass (moisture and air) and heat through porous elements, considering phase change and all heat transfer modes, including the radiative transfer through fibrous materials. Therefore, a new mathematical model, called CAR-H...

Predictions of physical phenomena in buildings are carried out by using physical models formulated as a mathematical problem and solved by means of numerical methods, aiming at evaluating, for instance, the building thermal or hygrothermal performance by calculating distributions and fluxes of heat and moisture transfer. Therefore, the choice of th...

Predictions of physical phenomena in buildings are carried out by using physical models formulated as a mathematical problem and solved by means of numerical methods, aiming at evaluating, for instance, the building thermal or hygrothermal performance by calculating distributions and fluxes of heat and moisture transfer. Therefore, the choice of th...

Moisture is one of the leading causes responsible for the worst of health conditions and energy performance in households and workplaces. To avoid it, the coupling between a combined heat, air and moisture (HAM) model and a CFD code becomes a crucial research topic to provide accurate results for real problems found in the building sector. Therefor...

Pixel counting (PxC) emerged as a powerful technique for external solar shading calculations of buildings, providing accurate results with great computational efficiency even for dense geometries. Motivated by this fact and because the technique can be also adapted to cope with interior surfaces without further ado, this paper aims at experimentall...

Clay-based materials are the most traditional components of buildings. To improve their performance in a sustainable way, agents can be mixed to fired clay acting as a pore-forming factor. However, firing temperatures highly influence their microstructure which is closely linked to a material’s final performance as a ceramic block. To highlight the...

It is well known that thermal insulation is a leading strategy for reducing energy consumption associated to heating or cooling processes in buildings. Nevertheless, building insulation can generate high expenditures so that the selection of an optimum insulation thickness requires a detailed energy simulation as well as an economic analysis. In th...

This work presents a detailed mathematical model combined with an innovative efficient numerical model to predict heat, air and moisture transfer through porous building materials. The model considers the transient effects of air transport and its impact on the heat and moisture transfer. The achievement of the mathematical model is detailed in the...

It is well known that thermal insulation is a leading strategy for reducing energy consumption associated to heating or cooling processes in buildings. Nevertheless, building insulation can generate high expenditures so that the selection of an optimum insulation thickness requires a detailed energy simulation as well as an economic analysis. In th...

This work presents an efficient numerical method based on spectral expansions for simulation of heat and moisture diffusive transfers through multilayered porous materials. Traditionally, by using the finite-difference approach, the problem is discretized in time and space domains (Method of lines) to obtain a large system of coupled Ordinary Diffe...

This work presents an alternative view on the numerical simulation of diffusion processes applied to the heat and moisture transfer through porous building materials. Traditionally, by using the finite-difference approach, the discretization follows the Method Of Lines (MOL), when the problem is first discretized in space to obtain a large system o...

This article describes the development of a new instructional design (ISD) to promote building energy simulation (BES) education. The study is based upon education fundamentals combined with computer-based learning and hypermedia to enable the development of a BES-based distance learning system. Some cognitive tools are established such as: (i) an...

The correct characterization of different materials assists in improving the results obtained via physical and numerical models. This study consists of the development of a numerical algorithm based on experimental data to obtain the spectral values of the index of refraction (n) and the coefficient of extinction (k) of several types of glasses ava...

Análise comparativa entre duas obras unifamiliares de alto padrão, que receberam os seguintes nomes: Residencia da Araucária Descampado (2013) e Residência Villacayo (2012)

It is of great concern to produce numerically efficient methods for moisture diffusion through porous media, capable of accurately calculate moisture distribution with a reduced computational effort. In this way, model reduction methods are promising approaches to bring a solution to this issue since they do not degrade the physical model and provi...

This pilot study aims to analyze the solar radiation transmission, daylight performance and glare reduction probability of complex shape solar control devices, developed with parametric modeling and digital fabrication. As methodology, initially the Rhinoceros3D+Grasshopper digital tools suite was used for the parametric modeling of solar control d...

This work presents an alternative view on the numerical simulation of diffusion processes applied to the heat and moisture transfer through multilayered porous building materials. Traditionally, by using the finite-difference approach, the discretization follows the Method Of Lines (MOL), when the problem is first discretized in space to obtain a l...

This work presents an efficient numerical method based on spectral expansions for simulation of heat and moisture diffusive transfers through multilayered porous materials. Traditionally, by using the finite-difference approach, the problem is discretized in time and space domains (Method of lines) to obtain a large system of coupled Ordinary Diffe...

One possibility to improve the accuracy of building performance simulation (BPS) tools is via co-simulation techniques, where more accurate mathematical models representing particular and complex physical phenomena are employed through data exchanging between the BPS and a specialized software where those models are available. This article performs...

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

A computational procedure known as co-simulation has been proposed in the literature as a possibility to extend the capabilities and improve the accuracy of building performance simulation (BPS) tools. Basically, the strategy relies on the data exchanging between the BPS and a specialized software, where specific physical phenomena are simulated mo...

External long-wave radiative heat transfer is a typical boundary condition problem in building physics and the solution of the Radiative Transfer Equation (RTE) involve important mathematical skills to apply a simple model and still nowadays the computational cost in algorithms for solving the integral-differential RTE is not explicit implemented i...

This paper presents an experimental validation procedure of two solar shading calculation techniques - pixel counting (PxC) and polygon clipping (PgC) - and an inter-software comparison to highlight the capabilities and efficiency of each solar shading calculation method. For the first purpose, digital images were taken from the surfaces of small-s...

Bringing advanced physics to building performance simulation (BPS) tools, by means of computational fluid dynamics (CFD) coupling, may enable significant improvement of accuracy on the prediction of energy consumption, thermal comfort, pollutant transport and mold growth risk. One of the challenges on coupling is the communication between whole-bui...

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

This book intends to stimulate research in simulation of diffusion problems in building physics, by first providing an overview of mathematical models and numerical techniques such as the finite difference and finite-element methods traditionally used in building simulation tools. Then, nonconventional methods such as reduced order models, boundary...

It is of great concern to produce numerically efficient methods for moisture diffusion through porous media, capable of accurately calculate moisture distribution with a reduced computational effort. In this way, model reduction methods are promising approaches to bring a solution to this issue since they do not degrade the physical model and provi...

This paper proposes the use of a Spectral method to simulate diffusive moisture transfer through porous materials as a Reduced-Order Model (ROM). The Spectral approach is an a priori method assuming a separated representation of the solution. The method is compared with both classical Euler implicit and Crank-Nicolson schemes, considered as large o...

This paper proposes the use of a Spectral method to simulate diffusive moisture transfer through porous materials as a Reduced-Order Model (ROM). The Spectral approach is an a priori method assuming a separated representation of the solution. The method is compared with both classical Euler implicit and Crank-Nicolson schemes, considered as large o...

Since the 1970s, due to the worldwide energy crisis, some countries have adopted severe legislation to promote energy efficiency in buildings. The electrical power utilized in buildings is directly related to the equipment required to provide thermal comfort to occupants. In this context, one of the most important factors that determine the choice...

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 rela...

This paper aims at estimating the sorption isotherm coefficients of a wood fiber material using experimental data. First, the mathematical model, based on convective transport of moisture, the Optimal Experiment Design (OED) and the experimental set-up are presented. Then, measurements of relative humidity within the material are carried out, after...

This paper presents a practical application of the concept of Optimal Experiment Design (OED) for the determination of properties of porous materials with in-situ measurements and an identification method. First, an experimental set-up was presented and used for the measurement of relative humidity within a wood fibre material submitted to single a...

This paper presents a practical application of the concept of Optimal Experiment Design (OED) for the determination of properties of porous materials with in-situ measurements and an identification method. First, an experimental set-up was presented and used for the measurement of relative humidity within a wood fibre material submitted to single a...

Implicit schemes require important sub-iterations when dealing with highly nonlinear problems such as the combined heat and moisture transfer through porous building elements. The computational cost rises significantly when the whole-building is simulated, especially when there is important coupling among the building elements themselves with neigh...

Implicit schemes require important sub-iterations when dealing with highly nonlinear problems such as the combined heat and moisture transfer through porous building elements. The computational cost rises significantly when the whole-building is simulated, especially when there is important coupling among the building elements themselves with neigh...

Moisture affects significantly the energy performance of air conditioning systems, the durability of materials, and the health of occupants. One way of reducing those effects, without increasing the energy costs, is by means of using porous material ability of absorbing and releasing moisture from/to the adjacent environment, which attenuates the i...

When comparing measurements to numerical simulations of moisture transfer through porous materials a rush of the experimental moisture front is commonly observed in several works shown in the literature, with transient models that consider only the diffusion process. Thus, to overcome the discrepancies between the experimental and the numerical mod...

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

Implicit schemes have been extensively used in building physics to compute the solution of moisture diffusion problems in porous materials for improving stability conditions. Nevertheless, these schemes require important sub-iterations when treating nonlinear problems. To overcome this disadvantage, this paper explores the use of improved explicit...

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...

An algorithm has been developed for the determination of incidence-angle dependent radiative properties and averaged properties of glazing systems based on simple performance indicators. First, the results are obtained using a computer code that applies statistical methods, multiple correlations for data treatment, and a mathematical approach to ob...

When comparing measurements to numerical simulations of moisture transfer through porous materials a rush of the experimental moisture front is commonly observed in several works shown in the literature, with transient models that consider only the diffusion process. Thus, to overcome the discrepancies between the experimental and the numerical mod...

The Brazilian state of Santa Catarina is responsible for more than 95% of the total bivalve mollusc production in Brazil, with the Pacific oyster being its second main product. The specie farmed along Santa Catarina´s coast is well adapted to the coastal environmental conditions, allowing oyster harvesting once a year. Nevertheless, the water tempe...

In the context of estimating material properties of porous walls based on in-site measurements and identification method, this paper presents the concept of Optimal Experiment Design (OED). It aims at searching the best experimental conditions in terms of quantity and position of sensors and boundary conditions imposed to the material. These optima...

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

The area of projected shadow on building facades may play a role of paramount importance in the prediction of solar energy conversion and building thermal and energy performance. Algorithms for solar shading calculations may directly affect the accuracy of results obtained by building energy simulation tools. In addition, the consideration of uncer...

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

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

In the context of estimating material properties of porous walls based on in-site measurements and identification method, this paper presents the concept of Optimal Experiment Design (OED). It aims at searching the best experimental conditions in terms of quantity and position of sensors and boundary conditions imposed to the material. These optima...

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

RESUME. La quantification et la propagation des incertitudes sont primordiales dans le processus de la comparaison mesure/simulation. Les sollicitations météorologiques conditionnent le comportement du bâtiment et le niveau d'incertitude associé à certaine variable météo pourrait induire des incertitudes significatives sur la réponse d'une platefor...

RESUME. Cet article présente une méthodologie basée sur les surfaces de réponse afin de produire une visualisation complète du comportement de la toiture en fonction de ses entrées les plus influentes. Ces entrées sont l'épaisseur d'isolation, la réflectivité solaire et l'émissivité thermique. La construction de la surface de réponse est réalisée v...

In this paper, the proper generalized decomposition (PGD) is used for model reduction in the solution of an inverse heat conduction problem within the Bayesian framework. Two PGD reduced order models are proposed and the approximation Error model (AEM) is applied to account for the errors between the complete and the reduced models. For the first P...

This paper presents a statistical approach for uncertainty and sensitivity analyses applied to 14 inputs whose 10 properties associated with brick material, using the four different EnergyPlus wall models. The variability of inputs has been extracted from several characterization works presented in IEA Annexes 14, 24 and 55, being coherent to the l...

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

The use of thermal insulation in roofing systems has been progressively increased in the last few years especially in emerging market countries to reduce energy consumption due to the more frequent use of air conditioners. However, moisture can meaningfully affect the performance of the roof and cause deterioration of the insulation as well as incr...

Moisture in porous building materials may reduce the structural integrity of building components. Although it is not an easy task, an elaborated knowledge of moisture transport in porous media is necessary to increase materials durability. Therefore the characterization of pore space is a vital and fruitful aspect of building physics. Thus permeabi...