The direct numerical simulation of blast waves (accidental or industrial explosions) is a challenging task due to the wide range of spatial and temporal scales involved. Moreover, in a real environment (topography, urban area. . .), the blast wave interacts with the geometrical obstacles resulting in reflection, diffraction and waves recombination phenomena. The shape of the front becomes complex, which limits the efficiency of simple empirical methods. This work aims at contributing to the development of a fast running method