Locally refined meshes are often inevitable for accurate, yet feasible computations. In the context of time-dependent PDEs, however, this comes at the cost that (due to the CFL condition) reducing the mesh width $\Delta x$ implies also that the timestep $\Delta t$ has to be reduced.
Relatively recently, Brian Vermiere proposed a family of Runge-Kutta methods that uses in refined part of the mesh explicit optimized/stabilized Runge-Kutta methods with higher number of stages, while in coarse regions Runge-Kutta methods with fewer stage evaluations are used.
Unfortunately, there are no details given in  regarding implementation and numerical analysis.
Therefore, I am looking for similar publications, where Runge-Kutta methods with different number of stages instead of locally reduced timesteps are used to compute locally refined problems.