一种通过混合分裂形式微分算子和广义熵投影的离散熵守恒/稳定通量重构格式
A Discretely Entropy Conserving/Stable Flux Reconstruction Scheme via Hybridized Split Form Differential Operator and Generalized Entropy Projection
- School of Aeronautics and Astronautics, Shanghai Jiao Tong University（上海交通大学航空宇航学院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文提出一种结合混合分裂微分算子与广义熵投影的离散熵守恒通量重构格式，适用于任意节点分布与修正函数，数值实验验证了其精度与熵稳定性。
AI中文摘要：
本文针对非线性守恒律提出了一种新颖的离散熵守恒/稳定通量重构（FR）格式。该格式将混合分裂形式微分算子与广义熵投影相结合，在不修改原始求积权重的情况下，实现了任意节点分布和任意修正函数的离散熵守恒。该公式直接建立在经典FR框架之上，并证明在保持守恒性质的同时，在半离散意义上实现熵守恒。使用等熵涡问题的数值实验证实了理论预测的精度，并展示了具有熵耗散界面通量的稳健熵行为。
英文摘要：
This paper proposes a novel discretely entropy conserving/stable flux reconstruction (FR) scheme for nonlinear conservation laws. The scheme combines a hybridized split-form differential operator with a generalized entropy projection, enabling discrete entropy conservation for arbitrary nodal distributions and arbitrary correction functions without modifying the original quadrature weights. The formulation is built directly upon the classical FR framework and is shown to preserve conservation properties while achieving entropy conservation in the semi-discrete sense. Numerical experiments using the isentropic vortex problem confirm the theoretically predicted accuracy and demonstrate robust entropy behavior with entropy-dissipative interface fluxes.
