Simulation of Steady Laser Hardening by an Arbitrary Lagrangian Eulerian Method

Abstract. One of the most practical methods for simulation of steady state thermal processing is the Arbitrary Lagrangian-Eulerian method. Each calculation step is split into two phases. In the first phase, the Lagrangian phase, the element mesh remains attached to the material. The evolution of the state variables is monitored and the state at the end of the phase is calculated. In the second phase, the Eulerian phase, the mesh is, broadly speaking, restored to its original position with respect to a window attached to the moving heat source. The mesh is not restored to its exact original position, but some allowance is made perpendicular to the flow direction in order to capture movement of the free surfaces. In this paper a finite element model for Lagrangian simulation of thermo-mechanical processes with phase transformations is combined with a second order discontinuous Galerkin method for modeling of Eulerian advection