Simulation numérique des traitements de surface par laser

This work deals with the numerical modeling of laser surface treatments, particularly laser remelting (a laser beam melts part of a moving work piece) and laser cladding (injection of powder in the melt pool produces a thin metallic layer on the work piece). A two-dimensional stationary model is presented for laser cladding. This model takes into account the solid-liquid phase change process and the important velocity field in the melt pool. A pure thermal problem is studied, which corresponds to a laser remelting model when the liquid particles movements are neglected. The enthalpy variable is introduced and thus the model reduces to solving the so-called stationary Stefan problem (a diffusion-convection equation, degenerated on the phase change interface). We present a Finite Element discretization for the corresponding regularized problem and give some a priori and a posteriori estimates. An efficient adaptive mesh algorithm is then presented. Finally we solve the complete laser cladding model (the two phase change and hydrodynamic problems) using a Finite Element Method and discuss some numerical results.