  In this paper, we apply the Paired-Explicit Runge-Kutta (P-ERK) schemes by
Vermeire et. al. (2019, 2022) to dynamically partitioned systems arising from
adaptive mesh refinement. The P-ERK schemes enable multirate time-integration
with no changes in the spatial discretization methodology, making them readily
implementable in existing codes that employ a method-of-lines approach.
  We show that speedup compared to a range of state of the art Runge-Kutta
methods can be realized, despite additional overhead due to the dynamic
re-assignment of flagging variables and restricting nonlinear stability
properties. The effectiveness of the approach is demonstrated for a range of
simulation setups for viscous and inviscid convection-dominated compressible
flows for which we provide a reproducibility repository.
  In addition, we perform a thorough investigation of the nonlinear stability
properties of the Paired-Explicit Runge-Kutta schemes regarding limitations due
to the violation of monotonicity properties of the underlying spatial
discretization. Furthermore, we present a novel approach for estimating the
relevant eigenvalues of large Jacobians required for the optimization of
stability polynomials.
