  We introduce a high-order space-time approximation of the Shallow Water
Equations with sources that is invariant-domain preserving (IDP) and
well-balanced with respect to rest states. The employed time-stepping technique
is a novel explicit Runge-Kutta (ERK) approach which is an extension of the
class of ERK-IDP methods introduced by Ern and Guermond (SIAM J. Sci. Comput.
44(5), A3366--A3392, 2022) for systems of non-linear conservation equations.
The resulting method is then numerically illustrated through verification and
validation.
