In the previous chapter we studied the implementation of boundary shock-ﬁtting for several problems. It is possible, see , to extend this technique to more complex problems. However, as the number of shocks increases, the method becomes increasingly complicated. Floating shock-ﬁtting was developed to circumvent this problem. As shown in Chapter 4 and , ﬂoating shock-ﬁtting works well for one-dimensional problems. For two-and three-dimensional problems, many of the operations (many of them being just simple bookkeeping) that are required to implement ﬂoating shock-ﬁtting remained cumbersome within the conﬁnes of structured grids. Thus, although several demonstrations of the method were made by Moretti [147,152] and other collaborators, the method has not been widely used. With the current level of maturity of unstructured grid methods, it now appears that ﬂoating shock-ﬁtting is a viable technique. The pioneering work in ﬂoating shockﬁtting with unstructured grids is part of a collaborative research effort originating at the University of Rome, La Sapienza, and the University of Basilicata, particularly in the work of Aldo Bonﬁglioli and Renato Paciorri .