  In this work, we develop a new hydrostatic reconstruction procedure to
construct well-balanced schemes for one and multilayer shallow water flows,
including wetting and drying. Initially, we derive the method for a
path-conservative finite volume scheme and combine it with entropy conservative
fluxes and suitable numerical dissipation to preserve an entropy inequality in
the semi-discrete case. We then combine the novel hydrostatic reconstruction
with a collocated nodal split-form discontinuous Galerkin spectral element
method, extending the method to high-order and curvilinear meshes. The
high-order method incorporates an additional positivity-limiter and is blended
with a compatible subcell finite volume method to maintain well-balancedness at
wet/dry fronts. We prove entropy stability, well-balancedness, and
positivity-preservation for both methods. Numerical results for the high-order
method validate the theoretical findings and demonstrate the robustness of the
scheme.
