The primary difference between the Eulerian model and the Lagrangian model is that in the Eulerian model nodes stay fixed and material moves inside the fixed mesh. While in the Lagrangian model, material position relative to nodes remains fixed. This is why the Lagrangian model is generally used to simulate the process outside the processed zone, while the Eulerian method is used to model the material flow.

Thus, in most studies, the workpiece is modelled using the Eulerian framework, while the welding tool is considered a Lagrangian rigid body. It should be further noted that in general the conservation equations in the Eulerian framework are written in terms of the spatial time derivative whereas for the Lagrangian framework of solid/structure analysis conservation equations are written using the material time derivative.