Laser welding of pure copper and its alloys is a challenging process with a growing industrial interest due to the latest development in the field of electric mobility. The difficulties are mainly related to the material's high thermal conductivity and a poor absorptivity of few percent at the classical IR laser (YAG). It is also well known that such a configuration can lead to the formation of undesirable defects, such as pores or spatters as a consequence of melt pool instabilities. It has been observed experimentally that the usage of a laser at both high speed and high power tends to limit those instabilities. Although this positive influence has already been observed for equivalent materials, a physical explanation is not yet available. In this perspective, a multiphysical simulation of the process at the melt pool scale is currently being developed by using comsol Multiphysics® software. The latter includes an Eulerian interface tracking method for the liquid-gas interface (phase field) and a ray-tracing description of the laser beam to take into account the well-known beam trapping effect under a keyhole regime. For the sake of time computation, the numerical model is first developed in an axisymmetric coordinate system (r,z) to be representative of a laser spot welding process and to validate the numerical coupling methodology. The model will then be extended to a 3D welding case and used as a predictive tool to make appropriate choices on welding parameters to obtain good quality welds (stable melt pool, low porosity rate, etc.).