An upwind numerical solution of nonlinear advection-diffusion problems with a moving heat source

In the present work, two-dimensional temperature variations and a position of a weldpool within a workpiece during keyhole plasma are welding are determined. The model allows to include temperature dependent thermal properties, variable welding speed, different keyhole radii and a nonlinear boundary condition of the third kind on the upper and the lower surfaces of the workpiece. The upwind scheme (donor cell method) is employed to present physically realistic numerical solutions. The obtained results can be used for controlling the plasma are welding process through the controlling of plasma jet diameter.