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.

我们针对弯曲三角网格上的二维浅水方程组（SWE），提出了一种高阶熵稳定不连续伽勒金（ESDG）方法。提出的方案保留了一个半离散的熵不等式，并为连续测深图保持了良好的平衡。我们提供了数值实验，证实了该方案的高阶精度和理论性质，并将所提出的方案与基于简单部分求和（SBP）有限差分算子的熵稳定方案进行了比较。最后，我们报告了在图形处理单元（GPU）上实现的计算性能，并与四边形网格上现有的GPU加速的高级DG方法的实现进行了比较。