  We present a high-order entropy stable discontinuous Galerkin (ESDG) method
for the two dimensional shallow water equations (SWE) on curved triangular
meshes. The presented scheme preserves a semi-discrete entropy inequality and
remains well-balanced for continuous bathymetry profiles. We provide numerical
experiments which confirm the high-order accuracy and theoretical properties of
the scheme, and compare the presented scheme to an entropy stable scheme based
on simplicial summation-by-parts (SBP) finite difference operators. Finally, we
report the computational performance of an implementation on Graphics
Processing Units (GPUs) and provide comparisons to existing GPU-accelerated
implementations of high-order DG methods on quadrilateral meshes.
