Non-disturbing Boundary Conditions for Modeling of Laser Material Processing

Surface laser treatment of a massive body is the typical geometry for various laser-assisted processes. The classical mathematical formulation is a heat source moving over the surface of a half-space target. Generally, such problems are numerically solved in a finite calculation domain. The adiabatic or isothermal boundary conditions are often applied at the boundaries of the calculation domain. Such an approach becomes rigorous when the linear size of the calculation domain is much greater than the size of the melt pool. It is time consuming. Economic non-disturbing differential boundary conditions proposed here are derived from the well-known analytical asymptotics for the steady-state temperature distributions around a moving heat source in 2D and 3D. Finite-difference boundary conditions approximating these differential conditions are tested for modeling of additive manufacturing of massive metallic parts and walls by selective laser melting. It is shown that the linear size of the calculation domain can be as small as double the size of the melt pool.