## 3 Fundamentals of CFD in the Context of Mechanical Processes
### Coupling with Other Simulation Tools (DEM, FEM, etc.) While CFD is a powerful tool for simulating fluid dynamics, heat and mass transfer, and hydrodynamic forces, its predictive capabilities can be substantially enhanced through coupling with complementary numerical methods. In food engineering, integration with approaches such as the DEM, FEM, population balance modeling, and data-driven algorithms allows for the simulation of multiphysics phenomena involving complex interactions among solid particles, fluids, deformable materials, and mechanical components. These hybrid modeling strategies are increasingly employed in the study and optimization of unit operations including mixing, extrusion, shaping, agglomeration, and drying [41]. Coupling CFD with DEM has proven particularly effective for systems involving particulate materials and fluid flow. DEM is a particle-based method that tracks the motion, collision, and contact forces of individual particles, while CFD models the surrounding fluid as a continuum. In the coupled CFD-DEM framework, the fluid phase is typically solved using an Eulerian approach, whereas the particle phase is described in a Lagrangian framework. Momentum exchange between the two phases is handled through interphase force models, including drag and pressure gradient terms. Applications in food processing include modeling mixing efficiency in solid-solid blenders, simulating fluidization behavior in drying chambers or spouted beds, and analyzing particle residence time and heat transfer in spray dryers. Despite its accuracy, CFD-DEM coupling is computationally demanding, especially when simulating large particle populations. Industrial-scale simulations often require the use of parallel computing and coarse-graining techniques to reduce the computational burden [9; 42]. The FEM, on the other hand, is well suited for modeling the mechanical response of soft or deformable food materials. FEM allows detailed simulation of stress-strain behavior, material deformation, and structural integrity during processing. Coupling CFD with FEM enables the simulation of fluid-structure interactions (FSI), where deformation of food matrices influences flow fields and vice versa. Such coupling is critical in modeling phenomena like die swell during extrusion, shrinkage and collapse during convective or vacuum drying, and the deformation of gels or flexible holds during shaping. These coupled problems can be approached using monolithic solvers that simultaneously solve governing equations for both fluid and solid domains or through partitioned methods that exchange boundary data between CFD and FEM solvers. Tools such as COMSOL Multiphysics and Abaqus are commonly used alongside CFD platforms to perform these analyses [43; 44]. Beyond DEM and FEM, other hybrid modeling strategies are gaining importance in food engineering. Coupling CFD with PBM (Population Balance Model) enables tracking of particle or droplet size distributions, coalescence, and breakage phenomena, which are essential in emulsification, crystallization, and agglomeration processes. CFD coupled with chemical kinetics allows for the simulation of simultaneous transport and transformation phenomena such as Maillard reactions, starch gelatinization, and protein denaturation during extrusion or thermal treatment. More recently, machine learning (ML) models have been trained on CFD-generated data to rapidly predict process outcomes and optimize operational parameters, significantly reducing computational requirements. Additionally, integration of CFD models with sensor data in real-time environments has facilitated the development of digital twin systems for predictive monitoring and control, aligning food manufacturing with Industry 4.0 paradigms [5; 45]. Despite the growing utility of coupled simulations, several challenges remain. These include high computational demands, particularly in fully coupled or transient simulations, as well as the difficulty of ensuring compatibility between different solvers or software platforms.