## 2 Meta-Analysis and Bibliometric Assessment  
Bibliometric analysis and meta-analysis are essential tools for understanding the evolution of scientific research, identifying trends, and mapping interconnections between studies. In the context of numerical simulations applied to FFF, these methods provide a structured evaluation of academic progress, technological advancements, and the role of computational modeling in optimizing additive manufacturing processes [16]. As FFF processes become increasingly complex, numerical simulations play a key role in predicting material behavior, improving mechanical performance, and refining process parameters [3].  
To evaluate this evolving landscape, a bibliometric analysis was conducted using a structured query applied to indexed databases. The search was designed to capture publications focused on fluid dynamics, structural modeling, and numerical methods within the scope of FFF. The query used was TITLE-ABS-KEY (additive AND manufacturing) AND TITLE-ABS-KEY (numerical AND methods) OR TITLE-ABS-KEY (numerical AND model) OR TITLE-ABS-KEY (simulation) AND TITLE-ABS-KEY (FFF) OR TITLE-ABS-KEY (FFF) AND PUBYEAR > 2004 AND PUBYEAR < 2026. The resulting dataset included 743 publications, which were processed using Scopus, structured with Excel and Power BI, and analyzed through VOS viewer to identify thematic clusters and research trends.  
A key focus of recent work has been the integration of fiber-reinforced polymers (FRPs) in FFF. From the initial dataset, ninety studies specifically addressed FRP-related simulations, examining the effects of short and continuous fibers on mechanical performance, deposition quality, and process optimization [5]. This thematic shift has gained momentum particularly since 2019 (see Figure 1), reflecting both technological innovations and a growing interest in advanced composite materials. The bibliometric findings (see Figure 2) show a significant increase in research related to FRPs, indicating that this field is changing quickly and becoming more active within FFF simulation studies.  
The reviewed literature was split into four main research areas: melt flow dynamics, which studies how polymers act during extrusion and deposition; cooling and solidification, which looks at heat loss and how it affects layer bonding and leftover stress; thermal-mechanical behavior, which examines stress buildup, warping, and shape changes in printed objects; and material property characterization, which evaluates how different polymer mixes and fiber-reinforced materials affect the final strength of printed parts. To support this analysis, a co-word analysis using VOS viewer showed the importance and connections of the main research topics in the FFF simulation area. The resulting network (see Figure 3) highlights clusters of frequently co-occurring terms, such as material behavior,  
Figure 1: Annual publications on FFF simulations (self-developed based on Scopus).  
Figure 2: Annual growth rate of FFF simulations (self-developed based on Scopus).  
process parameters, and testing, reflecting the multidisciplinary nature of the field and the growing synergy between computational techniques and experimental investigation.  
As the field grows, using detailed simulations, testing them in real life, and monitoring processes in real time will be crucial for making models more accurate and better at predicting outcomes. Future research should focus on creating consistent simulation methods, developing strong experimental testing techniques, and using machine learning to find defects, which will improve the accuracy, dependability, and scalability of FFF-based manufacturing processes. Future research should prioritize the standardization of simulation frameworks, the development of robust validation methodologies, and the incorporation of machine learning-based defect detection systems to enhance the precision, reliability, and scalability of FFF-based manufacturing processes.