  A recently introduced framework of semidiscretisations for hyperbolic
conservation laws known as correction procedure via reconstruction (CPR, also
known as flux reconstruction) is considered in the extended setting of
summation-by-parts (SBP) operators using simultaneous approximation terms
(SATs). This reformulation can yield stable semidiscretisations for linear
advection and Burgers' equation as model problems. In order to enhance these
properties, modal filters are introduced to this framework. As a second part of
a series, the results of Ranocha, Glaubitz, \"Offner, and Sonar ("Enhancing
stability of correction procedure via reconstruction using summation-by-parts
operators I: Artificial dissipation", 2016) concerning artificial dissipation /
spectral viscosity are extended, yielding fully discrete stable schemes.
Additionally, a new adaptive strategy to compute the filter strength is
introduced and different possible applications of modal filters are compared
both theoretically and numerically.
