  Scientists and engineers often create accurate, trustworthy, computational
simulation schemes - but all too often these are too computationally expensive
to execute over the time or spatial domain of interest. The equation-free
approach is to marry such trusted simulations to a framework for numerical
macroscale reduction - the patch dynamics scheme. This article extends the
patch scheme to scenarios in which the trusted simulation resolves abrupt state
changes on the microscale that appear as shocks on the macroscale. Accurate
simulation for problems in these scenarios requires extending the patch scheme
by capturing the shock within a novel patch, and also modifying the patch
coupling rules in the vicinity in order to maintain accuracy. With these two
extensions to the patch scheme, straightforward arguments derive consistency
conditions that match the usual order of accuracy for patch schemes. The new
scheme is successfully tested on four archetypal problems. This technique will
empower scientists and engineers to accurately and efficiently simulate, over
large spatial domains, multiscale multiphysics systems that have rapid
transition layers on the microscale.
