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.
翻译:在这项工作中,人们认为一种非保守平衡法的提法包括了干大气流动的旋转、压缩的 Euler 方程式。我们开发了一种半分辨的、可压缩的、对干大气流动的 Euler 方程式。我们开发了一种半分解的、稳定的不连续的Galerkin 法,用于使用对波动形式的数字通量的通量差异的概括化法。该方法使用了元素操作员的扭曲-环曲式配方,以确保即使在卷曲线藻上存在不完全融合的情况下,由此产生的离散性也是稳定的。一个、两个和三个维度的大气流动试验案例证实了理论的酶稳定性结果,并显示了该方法的高度精确性和稳健性。