## 1 Introduction  
Thermal energy storage systems can employ sensible or latent heat. Sensible heat storage technology is more widespread than latent heat storage; however, the use of latent heat storage presents the main advantage of a higher energy storage density [1]. Latent heat thermal energy storage with phase change materials (PCMs) has been extensively studied due to its potential in peak absorption both in energy demand and in energy supply [2]. The study of PCMs was popular during the energy crisis in the 1970s and 1980s, with the primary aim to use PCMs in solar thermal energy storage [3]. As a transient process, the time elapsed by the complete phase change of the PCM (charge or discharge) is essential to defining the viability of the latent heat thermal energy storage system (LHTESS). This period covered by charge or discharge can vary from low peak attenuation to daily base or long-term yearly base [4]. Therefore, the use of PCMs includes a wide range of applications, such as building passive climate control [5; 6; 7], concentrating solar power stations [8; 9; 10], electronic device thermal protection [11], textile products [12], and waste heat recovery [13; 14]. Several authors have reviewed PCMs with regard to their applications, materials, numerical models, and container shape. Thus, some significant parameters have been established [15] for the application and study of PCMs, such as desirable characteristics of materials, requirements of the LHTESS, initial classification of PCMs and latent heat measurement techniques. Additional contributions have been performed by [PERSON] et al. [16], [PERSON] et al. [1], [PERSON] et al. [2], and [PERSON] et al. [3]. More specifically, works [17; 18] are focused on PCMs for high-temperature applications, while [PERSON] et al. [19] have reviewed the group of metallic PCMs. [PERSON] and [PERSON] [20] have outlined the heat transfer characteristics for different size scales of encapsulation, as well as the effects of the PCM container material in the phase change process. [PERSON] and [PERSON] [21] focused their study on the melting process of PCMs and the effects of container shape on heat transfer and the melting process. [PERSON] and [PERSON] [22] and [PERSON] et al. [23] have analyzed the techniques adopted for thermal conductivity enhancement of thermal energy storage using PCMs. [PERSON] et al. [24] have recounted thermal energy storage systems with PCMs: the models were separated according to the first and second laws of thermodynamics. Regarding the numerical approach, [PERSON] et al. [16] and [PERSON] et al. [2] have outlined some characteristics of the formulations used to describe phase-change processes. [PERSON] et al. [25] and [PERSON] et al. [26] have reviewed several numerical studies of PCMs and have presented the characteristics of computational models according to the geometry of the PCM container. [PERSON] et al. [27] have analyzed the heat transfer mechanisms of phase change as well as analytical and numerical models for phase change. They reviewed PCMs consistently with the division into two categories: considering only heat conduction or considering conduction and convection simultaneously. [PERSON] [28] has pointed out physical phenomena associated with PCMs and has reviewed numerical methods used for modeling such phenomena. Some authors have presented specific reviews for numerical models, such as [PERSON] et al. [29] and [PERSON] et al. [30], in which phase change formulations and numerical procedures were pointed out. [PERSON] and [PERSON] [31] focused their study mainly on latent heat formulation. [PERSON] and [PERSON] [32] have reviewed numerical models for the velocity transition between solid and liquid and performed tests and comparisons between different models. Despite the large number of review papers regarding PCMs, very few are specifically about numerical modeling features. Among these reviews, the most common approach is to focus on latent heat modeling or velocity transition modeling.