  We propose a novel approach to approximate numerically shock waves. The
method combines the unstructured shock-fitting approach developed in the last
decade by some of the authors, with ideas coming from embedded boundary
techniques. The numerical method obtained allows avoiding the re-meshing phase
required by the unstructured fitting method, while guaranteeing accuracy
properties very close to those of the fitting approach. This new method has
many similarities with front tracking approaches, and paves the way to
shock-tracking techniques truly independent on the data and mesh structure used
by the flow solver. The approach is tested on several problems showing accuracy
properties very close to those of more expensive fitting methods, with a
considerable gain in flexibility and generality.
