Sonic boom assessment methods through numerical analysis have been ever-evolving since the development of the fundamental theory. With the growing need for efficient low-boom design tools and the increasing computational resources, original approaches using advanced numerical simulation techniques have been developed. Among the various existing methods, the three layer resolution introduced in the 1990's is very convenient for low-boom aircraft design. It is based on near-field CFD calculation which is matched with the far-field propagation code using a description of the source using multipoles before undergoing classical acoustic propagation through atmosphere. The following paper reviews the theory of the near to far-field matching as well as the different resolution approaches and their limits. The impact of the resolution method on the ground propagated signal is also presented.