In this work a non-conservative balance law formulation is considered that encompasses the rotating, compressible Euler equations for dry atmospheric flows. We develop a semi-discretely entropy stable discontinuous Galerkin method on curvilinear meshes using a generalization of flux differencing for numerical fluxes in fluctuation form. The method uses the skew-hybridized formulation of the element operators to ensure that, even in the presence of under-integration on curvilinear meshes, the resulting discretization is entropy stable. Several atmospheric flow test cases in one, two, and three dimensions confirm the theoretical entropy stability results as well as show the high-order accuracy and robustness of the method.

在这项工作中，考虑了一个非保守平衡定律公式，其中包含干燥大气流动的旋转、可压缩欧拉方程。我们在曲线网格上开发了一种半离散熵稳定不连续 Galerkin 方法，该方法使用波动形式的数值通量的通量差分的推广。该方法使用单元算子的倾斜混合公式来确保即使在曲线网格上存在欠积分的情况下，所得的离散化也是熵稳定的。几个一维、二维和三维的大气流动测试案例证实了理论熵稳定性结果，并展示了该方法的高阶精度和鲁棒性。