Moretti's shock-fitting methods on structured and unstructured meshes

Over the last 25 years shock-fitting methods have been almost completely abandoned and replaced by the prevailing shock-capturing methods. Only a few research groups have continued to use and to develop these techniques. A few months after the death of Gino Moretti, the man who contributed to the development of shock-fitting methods from the 1960s until the 1980s, it is useful to describe the state-of-the-art of these methods, from the techniques developed for structured meshes up to recent developments for unstructured grids. The chapter aims to spread knowledge of these little known techniques, especially among the latest generations of CFDers that grew up in a context exclusively dominated by shock-capturing methods.