*2.1. Building Thermal-Performance Modelling*

Physical models are used to simulate the thermal performance of various buildings with their own special demands and uses, e.g., dwellings, offices, schools, etc. These models involve interpreting of space heating [8], natural ventilation [9], air conditioning systems [10], solar-thermal systems [11], Photovoltaic panels [12], occupants' behaviour [13,14], etc. The physical modelling techniques are based mainly on the solving of heat transfer equations.

To solve such physical problems, numerous simulation software packages are available, many of them also associated by benchmarking activities performed by many authors and researchers. Theoretically, each building software is able to include thermal physical phenomena encountered in buildings. Most computational tools provide the choice to users to select the physical mechanisms and the associated equations required. There are two major building thermal models' categories most commonly used [15] (mainly in the framework of research activities and projects):


The present paper focuses on the application of the multi-zonal method in case of building energy simulation and provides an extensive presentation of the principles of this method and available computational tools to assess building energy performance. As far as field models are concerned, this paper focuses on their uses for simulating the urban microclimate. Therefore, the overview of field modelling principles and computational tools is restricted herein mainly to open spaces (Section 2.2), while only a short presentation of their uses for indoor airflows and building thermal simulation is provided.

#### 2.1.1. Field Models for Indoor Airflow Assessments

The most complete field modelling approach in building thermal simulation is (so far) the CFD method. This is a "microscopic" approach of heat transfer modelling providing a detailed resolution of the airflow pattern. It is based on the discretization of a building zone into control volumes in the form of structured or unstructured mesh [16]. The CFD approach is essentially based on the solution of the so-called Navier–Stokes equations. A large number of CFD software exists such as Ansys Fluent, Ansys CFX, COMSOL Multi-physics, MIT-CFD, Phoenics, etc., most of them possessing additional capabilities to simulating indoor airflows and building thermal behaviour. They are general-purpose CFD platforms and can be applied to every system involving fluid flow phenomena. The CFD method is mainly employed for its ability to solve for mass, momentum, heat, chemical

species, and turbulence parameters' conservation equations. While available software present similar characteristics in terms of the conservation equations solved or on the mathematical formulation of boundary conditions (for example, Dirichlet or Neuman formulations), some of them differ on the equations' discretization method or on the solver used for processing the algebraic system of discretized differential conservation equations. There are three fundamental methods for discretization purposes: The Finite Difference (FDM), the Finite Volume (FVM), and the Finite Element Method (FEM). These methods present different precision and numerical efforts, but they are all based on the discretization of Navier–Stokes equations. On the other hand, the treatment of boundary conditions in these methods is still a key issue in fluid flow numerical simulations depending on the engineering application studied. Indeed, in non-isothermal fluid flows, where design parameters or physical properties have fluctuations, boundary conditions require special treatment. This has led to enhancements of numerical methods, for example, on the basis of fluctuation-based equations, the so-called Stochastic Finite Element Method (SFEM), which was introduced and exercised in benchmark fluid-flow case studies by Kami ´nski and Carey [17].

The CFD analysis produces a detailed description of the airflow field within indoor environments including velocity vector distribution (magnitude and direction), temperature distribution, chemical species dispersion, etc. The prediction of the aforementioned properties of the flow field is very useful even in the early design stages as it reveals areas with unpleasant droughts and thermal discomfort (refer, for example, to ref. [18]) and areas of pollutants' confinement, for different design alternatives. Hence, it helps the building design practitioner to review and decide the best among the design alternatives. The main disadvantage of the CFD method, however, still is the high computational time required to solve accurately for the conservation equations in full 3D geometries adopting fine meshes respecting the grid-independent solution principle [19] as far as possible. However, given that the airflow in at least 75% of the building volume is almost stagnant (velocity magnitude below 0.5 m/s) [15], it is not always necessary to apply the CFD approach for the entire building but only to certain parts, e.g., within spaces affected by installed Heating Ventilating and Air-Conditioning (HVAC) systems or within naturally ventilated spaces. This allows reducing computational time significantly. For this reason, the CFD is frequently coupled with less time-consuming multi-zonal techniques or other statistical ones. Tan and Glicksman [20] compared the full CFD simulation results with those obtained by the coupling between CFD and a multi-zonal tool for captivating natural ventilation through large openings or an atrium. It was demonstrated that the latter required 10 times less duration of computations until full convergence in relation to the full CFD method, exhibiting similar accuracy. Kato [21] provided an extended review of coupled CFD and zonal or network techniques and applications in building heat-transfer simulations and reported the required theoretical conditions for reliable coupled simulations, balancing fidelity in predictions and reasonable computational times and resources.
