## Fixed Grid Numerical Models for Solidification and Melting of Phase Change Materials (PCMs)  
**[PERSON] 1, [PERSON] 1, [PERSON] 1, [PERSON] 2,* and [PERSON] 2**  
1 Mechanical Engineering Graduate Program, Universidade do Vale do Rio dos Sinos, Sao Leopoldo 93022-750, Brazil; [EMAIL_ADDRESS] (J.H.N.E.); [PERSON]DDRESS] (R.D.C.O.); [EMAIL_ADDRESS] (L.A.O.R.)  
2 Department of Industrial Engineering (DIN), School of Engineering and Architecture, Alma Mater Studiorum, University of Bologna, Viale Risorgimento 2, 40136 Bologna, Italy; [EMAIL_ADDRESS]  
* Correspondence: [EMAIL_ADDRESS]; Tel.: +39-051-2093293  
Received: 2 September 2019; Accepted: 8 October 2019; Published: 15 October 2019  
Phase change materials (PCMs) are classified according to their phase change process, temperature, and composition. The utilization of PCMs lies mainly in the field of solar energy and building applications as well as in industrial processes. The main advantage of such materials is the use of latent heat, which allows the storage of a large amount of thermal energy with small temperature variation, improving the energy efficiency of the system. The study of PCMs using computational fluid dynamics (CFD) is widespread and has been documented in several papers, following the tendency that CFD nowadays tends to become increasingly widespread. Numerical studies of solidification and melting processes use a combination of formulations to describe the physical phenomena related to such processes, these being mainly the latent heat and the velocity transition between the liquid and the solid phases. The methods used to describe the latent heat are divided into three main groups: source term methods (E-STM), enthalpy methods (E-EM), and temperature-transforming models (E-TTM). The description of the velocity transition is, in turn, divided into three main groups: switch-off methods (SOM), source term methods (STM), and variable viscosity methods (VVM). Since a full numerical model uses a combination of at least one of the methods for each phenomenon, several combinations are possible. The main objective of the present paper was to review the numerical approaches used to describe solidification and melting processes in fixed grid models. In the first part of the present review, we focus on the PCM classification and applications, as well as analyze the main features of solidification and melting processes in different container shapes and boundary conditions. Regarding numerical models adopted in phase-change processes, the review is focused on the fixed grid methods used to describe both latent heat and velocity transition between the phases. Additionally, we discuss the most common simplifications and boundary conditions used when studying solidification and melting processes, as well as the impact of such simplifications on computational cost. Afterwards, we compare the combinations of formulations used in numerical studies of solidification and melting processes, concluding that \"enthalpy-porosity\" is the most widespread numerical model used in PCM studies. Moreover, several combinations of formulations are barely explored. Regarding the simulation performance, we also show a new basic method that can be employed to evaluate the computing performance in transient numerical simulations.  
phase change materials (PCMs); computational fluid dynamics (CFD); melting and solidification processes; computational performance