Fourth Generation models are distinguished by adding the equations of fluid dynamics to the modeling of the weld heat source.

Recall that the First, Second and Third Generation models have no fluid velocity. The most general equations for macroscopic fluid dynamics are the Navier-Stokes equations. They can include buoyancy and Lorentz forces acting on the interior of the liquid phase. Marangoni effect forces, pressure and shear forces from the arc act on the surface of the weld pool. Some models include some form of droplet flow from a consumable electrode. However, as arc welding currents rise much above 100 to 150 amps, most of these models have difficulty accounting for what appears to be chaotic motion in the weld pool and possibly chaotic and possibly turbulent motion coupling the velocity, pressure and temperature of the liquid in the weld pool and velocity, pressure, temperature, voltage and current density in the arc. To the author's knowledge, the current state of the art of Fourth Generation models that couple heat equation with the transient Navier-Stokes equations has not pushed past this barrier. On the other hand, Sudnik [25 and 26] has developed models for deep penetration laser welds that contain a few, say three, functions describing the velocity field in a laser weld pool. He calibrates these models with experimental observations to estimate a few coefficients or fitting parameters in the model. These models are very robust and require very little computing power or time. Because they are correlated with experimental data they are expected to be accurate for the ranges of welds for which they were fitted. The price to be paid is the cost of the experiments needed to determine the correlation coefficients.