Numerical Stabilization of the Melt Front for Laser Beam Cutting

The Finite Difference Element Method (FDEM) is a black-box solver that solves by a finite difference method arbitrary nonlinear systems of elliptic and parabolic partial differential equations (PDEs) on an unstructured FEM grid in 2D or 3D. For each node we generate difference formulas of consistency order q with a sophisticated algorithm. An unprecedented feature for such a general black-box is the error estimate that is computed together with the solution. In this paper we present the numerical simulation of the laser beam cutting of a metal sheet. This is a free boundary problem where we compute the temperature and the form of the melt front in the metal sheet. During the cutting process, the numerical stabilization of the melt front is a great challenge.