  3D free boundary equilibrium computations have recently been used to model
external kinks and edge harmonic oscillations (EHOs), comparing with linear MHD
stability codes, and nonlinear analytic theory [Kleiner et al, PPCF 61 084005
(2019)]. In this study, results of the VMEC equilibrium code are compared
further with nonlinear reduced MHD simulations, using the JOREK code. The
purpose of this investigation is to understand the extent to which the
modelling approaches agree, and identify the important physical effects which
can modify the dynamics. For the simulated external kink, which is dominated by
a single toroidal harmonic, good agreement is found when a large Lundquist
number is used in the JOREK simulation, such that resistive effects are
sub-dominant. Modelling EHOs where multiple toroidal harmonics are linearly
unstable, the saturated perturbation observed can differ in the dominant
toroidal harmonic. On the ideal timescale, a n=2 EHO is observed in JOREK,
while the saturated perturbation predicted by VMEC is a n=1 mode. Extending
simulations into timescales where resistive effects can play a role, similar
n=1 perturbations can be found. The coupling of different linearly unstable
toroidal harmonics in the JOREK simulation broadens the magnetic energy
spectrum and ergodises the plasma edge region, resulting in a more localised
pressure perturbation. These effects are not observed in VMEC, because closed
magnetic flux surfaces are enforced. Despite the sensitivity of JOREK results
on the assumed resistivity, saturated states can be found using both approaches
that are in reasonable agreement, even for this more advanced case.
