Keyhole laser beam welding (LBW) of stainless steel sheets with a gap in between is numerically simulated with a three-dimensional, transient multi-physical model for laser material processing. At first, the model’s ability to reproduce experimental results on a relatively coarse computational mesh within reasonable computing time, so as to serve as process optimization tool, is presented. An example of process optimization, where a given set of weld seam quality criteria is fulfilled by iteratively optimizing a secondary laser beam, is shown. The relatively coarse mesh, in combination with a good model calibration to the experimental conditions, allows for sufficiently fast simulations to use this approach for optimization tasks. Finally, using a finer spatial and temporal discretization, the dynamic processes in the vicinity of the keyhole leading to the formation of pores are investigated. The physical phenomena predicted by the simulation are coherent with experimental observations found in literature.