Experiments have shown that wild type P. aeruginosa swarms much faster than rhlAB mutants on 0.4% agar concentration surface. These observations imply that development of a liquid thin film is an important component of the self-organized swarming process. A multiscale model is presented in this paper for studying interplay of key hydrodynamical and biological mechanisms involved in the swarming process of P. aeruginosa. This model combines a liquid thin film equation, convection-reaction-diffusion equations and a cell-based stochastic discrete model. Simulations demonstrate how self-organized swarming process based on the microscopic individual bacterial behavior results in complicated fractal type patterns at macroscopic level. It is also shown that quorum sensing mechanism causing rhamnolipid synthesis and resulting liquid extraction from the substrate lead to the fast swarm expansion. Simulations also demonstrate formation of fingers (tendrils) at the edge of a swarm which have been earlier observed in experiments.