2.1.2. The Multi-Zonal (Nodal) Approach

The multi-zonal approach assumes that each building zone is a homogeneous volume with uniform state variables. Thus, each zone is approximated as a node with a unique flow property, e.g., temperature, pressure, pollutant concentration, etc. Generally, a computational node stands for a room, a wall, or the exterior of the building, to which specific loads, such as internal occupancy, equipment gains, heat sources, etc., are allocated. The heat transfer equations are solved for each node and it can be considered as a onedimensional approach. In international literature, one can find two main methods used for the multi-zonal approach [15]:


Most available software is designed based on the former technique. The latter method is applied for nodal approaches through the representation of heat transfer from electrical analogy, which was introduced by Rumaniovski et al. [22]. The usefulness of this method lies in the fact that it drastically simplifies the mathematical representation of the physical problem through the linearization of conservation equations, leading to reduced computational time.

The major advantage of this method is that it describes the behaviour of a building with many zones on a large time scale within modest computational resources. It is a particularly well-adopted technique for energy-consumption estimations and of the dynamic changes of space-averaged temperature into a room. In addition, it is useful to estimate air-change rates and the distribution of airflow properties among different rooms. Ventilation efficiency or pollutant transport in buildings can also be studied by this method [23].

Due to the zero-spatial-gradient assumption regarding the airflow state variables within a node, the multi-zonal method presents the following limitations:


According to Kato (2018) [21], one effective way to "heal" the aforementioned limitations is through CFD nodal-coupled simulations. CFD and network-model coupled simulation is particularly useful when ventilation effectiveness of a large indoor space is required to be included in the energy simulation for long-term use. In this case, the nodal model serves as the boundary conditions' generator for the CFD model, which then undertakes the solution of the airflow field within the building zone at each user-defined time step.

One additional limitation acknowledged in the common multi-zonal approach is that the effects of air infiltration through openings, cracks, etc. are not adequately addressed. Indeed, most computational tools for building energy simulation incorporate mainly empirical correlations and default infiltration rates depending on different leakage properties of the building envelope. On the other hand, it is true that air infiltration is a case-sensitive issue, which requires appropriate modelling treatment to account for windand/or buoyancy-driven air movement through openings and cracks. It is also true that intervention measures referring to air tightness and consequent infiltration may lead to high amounts of energy savings related to heating/cooling. For instance, simulations of a large number of building types document that reducing air leakage can save 5–40% of heating and cooling energy [24]. An extensive investigation involving real-scale measurements of air leakage in 129 single and multi-family houses in Spain revealed mean air-change rates of 6.1 h−<sup>1</sup> for single-family dwellings and 7.1 h−<sup>1</sup> for multi-family housing, which advocate relatively high contributions to the energy consumption of the tested buildings [25]. Considering the fact that air infiltration greatly affects buildings' energy consumption as well as the accuracy of simulation predictions in terms of heating and cooling loads, thus the predicted energy consumption, it deserves a great deal of attention in simulation environments. Han et al. [26] explored different modelling strategies of infiltration rates

for an office building and compared their performance in terms of predictions' accuracy. They proposed a coupled approach associated with time-dependent infiltration rates by integrating multi-zone airflow modeling and CFD results into energy simulations. It was demonstrated that the suggested simulation method provides improvement of the accuracy of energy simulations with up to 11% reduction of the root mean square error and of the normalized mean bias error. Prescribing air-tightness interventions, among other envelope interventions, in higher education buildings in Egypt, total energy savings of up to 33% were documented using the multi-zonal simulation approach [27].

#### 2.1.3. Collation of Simulation Methods

The previous paragraphs described the two major methods to deal with building physics' modelling. The CFD method provides a detailed view of the physical mechanisms occurring in building systems. It is particularly adopted to solve for the convective phenomenon that takes place in large building spaces. In such spaces, the convective phenomenon, which causes airflow parameters' non-uniformity, is well analyzed, providing an accurate prediction of the Convective Heat Transfer Coefficient (CHTC) and, thus, of heat transfer. On the contrary, the multi-zonal approach underestimates CHTC and other variables' heterogeneity in these specific cases. However, it should be pointed out that it is difficult to conduct entire building simulations using CFD due to the associated high computational time and resources. Alternatively, coupled CFD with a multi-zonal model can be used.

On the other hand, the multi-zonal method is really well adopted to treat global building physics' resolution, assuming a uniform airflow field in each thermal zone. The main objective of this method is to simplify the algebraic system by linearizing a large part of the governing conservation equations (when it is physically accepted). As a result, the technical complexity is substantially reduced and so is the required time of computations. The multi-zonal method is more appropriate when more "macroscopic" effects are of interest, such as building energy consumption, rather than when the airflow pattern is the main goal. It should be mentioned, however, that the airflow properties' variations significantly affect indoor–outdoor interactions and, in this way, the envelope thermal behaviour as well as air infiltration rates. This causes variations in systems' operation schedules, which, in turn, influence building energy consumption. In this sense, the computational tool or method used to conduct a building energy study requires experience to understand which tool is more appropriate or to know when coupled multizonal/field modelling approaches are required for more accurate and reliable studies. A summary of the capabilities of the methods discussed above is reported in Table 1.

**Table 1.** Collation of major building physics' simulation methods.


It should be clarified that the techniques described above need input parameters, such as the meteorological data, thermo-physical properties of the building envelope, occupancy parameters, systems' operating schedules, etc. Obviously, all these parameters are interpreted with a degree of uncertainty. In addition to these uncertainties, there

are certain assumptions adopted in order to reduce the complexity of building physical mechanisms. The combination of uncertainties in interpreting collected data (physical properties, materials, and occupancy-related) with the adoption of assumptions often leads to discrepancies between the simulated results and reality. The major challenge scientists and engineers currently face is to reduce uncertainties without compromising simulations' time, practicability, and accuracy. One major source of uncertainty in building energy analysis is the end users' behaviour, considering the fact that, ultimately, the building consumes energy in accordance with the habits of occupants over building systems. Hence, it is important to realize that, in view of realistic building energy simulation, the setup of systems' operation schedules should reflect occupants' behaviour as accurately as possible. Motivated by the discrepancy between the measured and the calculated heat consumption of residential buildings, Hansen et al. [28] investigated heat-related habits of occupants, utilizing extensive questionnaire surveys, and correlated practices of adjusting thermostats, clothing conditions, perceived thermal comfort, building envelope, and systems' installations. Their study demonstrated that material arrangements substantially affect occupant expectations and practices, associated with increased indoor temperatures and energy demand. The behavioral effect is evident even in more stable buildings, such as office buildings, as presented by Liu et al. [29]. They conducted a field study in office buildings in the UK and concluded that the adaptive behaviors of occupants showed substantial seasonal and daily variations. It was shown that non-physical parameters such as habit affect the adaptive responses of occupants, sometimes yielding to absurd behavior, which could lead to increased use of energy. The key delivery of the study was the illustration of how occupants would adapt and interact with their built environment, which can be adopted in building retrofitting strategies or in energy management systems for comfortable built environments. The aforementioned studies, but also many others (for example those reported in ref. [30]), suggest that any simulation method, either multi-zonal, CFD, or other, should account for building systems' operation schedules reflecting realistic end users' behaviors. This means that accessibility to building systems' operation schedules is a prerequisite of the computational tool used for energy simulations.

As far as computational time is concerned, several solutions consisting of reducing system size exist in the scientific literature (refer, for example, to refs. [31,32]. Another idea is to reduce the detail of building geometry by merging rooms or merging walls. Such simplifications should speed up significantly the solution process. Generally, an important limitation of the physical formulation is the need for a detailed description of the physical behaviour. Therefore, it implies detailed knowledge of the physical processes, especially of the ones occurring in the interior and the exterior of the building geometry. Within the scope of this paper is to help designers in understanding better the available methods to assess building energy performance and in identifying the most appropriate computational tools in order to balance accuracy and practicability in terms of easiness to use and of calculation time. In the next subsection the most popular and widely used building energy (mainly multi-zonal) simulation tools are described, highlighting their strengths and weaknesses.
