发表机构
Johannes Gutenberg University Mainz; Australian National University; Leibniz Institute for Tropospheric Research (TROPOS)（约翰内斯·古腾堡美因茨大学; 澳大利亚国立大学; 莱布尼茨对流层研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对向量不变形式的可压缩欧拉方程，提出熵稳定且对等温、等熵背景态良好平衡的DGSEM方法，守恒熵与总能量，适用于大气流动动力学核心。
AI 中文摘要
我们在通量差分间断伽辽金谱元方法（DGSEM）框架内，针对向量不变形式且以位温作为预报变量的带重力可压缩欧拉方程，发展了结构保持方法。通过将非守恒项离散为对称和反对称乘积，我们推导出同时守恒热力学熵和总能量的两点数值通量。此外，我们设计了一种对等温背景态和等熵背景态均具有良好平衡性的熵稳定数值通量。所有性质均被证明可推广到一般曲线网格上的高阶DGSEM。多个数值算例证实了理论发现，并展示了该格式在现代大气流动动力学核心中的鲁棒性和准确性。
英文摘要
We develop structure-preserving methods for the compressible Euler equations with gravity in vector-invariant form and potential temperature as a prognostic variable within the flux-differencing discontinuous Galerkin spectral element method (DGSEM) framework. By discretizing the nonconservative terms as symmetric and antisymmetric products, we derive two-point numerical fluxes that conserve both the thermodynamic entropy and the total energy. Moreover, we design an entropy-stable numerical flux that is well-balanced for both isothermal and isentropic background states. All properties are shown to carry over to the high-order DGSEM on general curvilinear meshes. Several numerical examples confirm the theoretical findings and show the robustness and accuracy of the scheme for use in modern dynamical cores for atmospheric flows.
CommentsReproducibility repository: https://github.com/MarcoArtiano/2026_entropy_stable_vector_invariant
