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Abstract This study presented a comprehensive computational fluid dynamics-based model for fused filament fabrication (FFF) three-dimensional (3D) printing multiphase and multiphysics coupling. A model based on the framework of computational fluid dynamics was built, utilizing the front-tracking method for high precision of multiphase material interfaces, a fully resolved simulation at the mesoscale explores the underlying physical mechanism of the self-supported horizontal printing. The study investigated the influence of printing temperature and velocity on the FFF process, exhibiting a certain self-supporting forming ability over a specific range. The results indicated that during the printing of large-span horizontal extension structures, the bridge deck material transitions from initial straight extension to sagging deformation, ultimately adopting a curved shape. The straight extension distance is inversely proportional to the depth of the sagging deformation. Additionally, the study revealed that printing temperature primarily affected the curing time of the molten material, while printing velocity fundamentally affected the relaxation time of both thermal and dynamic characteristics of the material.