  In this paper, we introduce a methodology to design genuinely two-dimensional
(2D) secondorder path-conservative central-upwind (PCCU) schemes. The scheme
studies dam-break with high sediment concentration over abrupt moving
topography quickly spatially variable even in the presence of resonance. This
study is possible via a 2D sediment transport model (including arbitrarily
sloping sediment beds and associated energy and entropy) in new generalized
Shallow Water equations derived with associated energy and entropy in this
work. We establish an existence theorem of global weak solutions. We show the
convergence of a sequence of solutions of the proposed model. The second-order
accuracy of the PCCU scheme is achieved using a new extension AENO (Averaging
Essentially Non-Oscillatory) reconstruction developed in the 2D version of this
work. We prove by rigorous demonstrations that the derived 2D scheme on
structured meshes is well-balanced and positivity-preserving. Several tests are
made to show the ability and superb performance of the proposed numerical
modeling. The results obtained are compared with those existing in the
literature and with experimental data. The current modeling improves some
recent results in sediment transport and shows a good ability to simulate
sediment transport in large-range environments.
