| Calculation of heat, mass, and momentum transfer | Part scale heat conduction model | Fourier heat conduction equation is solved either analytically in 1D or 2D or numerically in 3D | Temperature fields; fusion zone geometry; cooling rates |
| Part scale heat transfer and fluid flow | Solves 3D transient conservation equations of mass, momentum, and energy | Temperature and velocity fields; fusion zone geometry; cooling rates; solidification parameters; lack of fusion |
| Part scale volume of fluid and level set methods | Tracks the free surface of the molten pool; computationally intensive; accumulates errors and the calculated deposit shape and size often do not agree well with experiments | 3D deposit geometry; temperature and velocity fields; cooling rates; solidification parameters |
| Powder-scale models | Involves free surface boundary conditions treating thermodynamics, surface tension, phase transitions, and wetting; small timescale and length scale, computationally intensive | Temperature and velocity fields; track geometry; lack of fusion; spatter; surface roughness |
| Microstructure, nucleation, and grain growth prediction | TTT-based, CCT-based, and JMA-based models | Based on phase transformation kinetics during cooling; widely used for simulating phase transformations in steels and common alloys; high computational efficiency | Solid-state phase transformation kinetics |
| Monte Carlo method | A probabilistic approach of grain orientation change; provides grain size distribution with time; high computational efficiency | Grain growth; solidification structure; texture |
| Cellular automata | Simulates growth of grain and subgrain structure during solidification; medium accuracy and computational efficiency | Solidification structure; grain growth; texture |
| Phase field model | Simulates microstructural features and properties by calculating an order parameter based on free energy that represents the state of the entire microstructure; computationally intensive | Nucleation; grain growth; evolution of phases; precipitate formation; solid-state phase transformation |
Calculation of residual stresses and distortion | FEA-based thermomechanical models | Calculation of residual stresses and distortion FEA-based thermomechanical models solves 3D constitutive equations considering elastic, plastic, and thermal behavior; many software packages exist, and these are easy to implement and can handle intricate geometries; adaptive grid and inherent strain method are often used to increase calculation speed | Evolution of residual stress; strains; distortion; delamination; warping |