AI 中文总结
研究双曲系统有源通量型格式的熵稳定性，构建保界、非振荡且熵递减的整体格式，在特定测试案例上测试，证明熵修正有效，该方法可用于多边形网格。
AI 中文摘要
本文致力于分析配备一个熵不等式的双曲系统的有源通量型格式的熵稳定性性质。这类格式涉及两组自由度：覆盖计算域的单元边界上选取的点值以及这些单元内解的平均值。研究表明只需得到平均值的熵不等式，点值自由度不起作用。构建了一种整体格式，它具有保界性、非振荡性且熵递减。熵条件在Tadmor框架中实现，仅针对半离散格式。该格式在对熵不等式满足情况敏感的Kurganov - Popov - Petrova测试案例上进行了测试，结果表明熵修正有效。虽以三角形版本进行开发、实现和测试，但同样方法可用于多边形网格。
英文摘要
This paper is devoted to the analysis of the entropy stability properties of Active Flux\yolo{-type} scheme for a hyperbolic system equipped with one entropy inequality. This type of scheme evolves two sets of degrees of freedom: point values that are chosen on the boundary of the elements that cover the computational domain, and the average of the solution in these elements. We show that the only thing to do is to get an entropy inequality for the average values, the point values degrees of freedom do not play any role. We construct a monolithic scheme which is bound preserving of \cite{BP_Pampa_VEM}, non oscillatory following \cite{PampaDG}, and entropy diminishing. The entropy condition is implemented in Tadmor's framework\cite{TadmorEntropy}, i.e. for the semi-discrete scheme only. The scheme is tested on the Kurganov-Popov-Petrova test case \cite{KPP} which is known to \yolo{be} sensitive to the satisfaction of an entropy inequality. We show that our entropy correction is effective: if we do not activate the bound-preserving nor the non oscillatory condition, we get the correct solution with some spurious wiggles, as expected. Though the development, implementation and tests are done with the triangle version of the scheme, the same method can be used for polygonal meshes, following \cite{BP_Pampa_VEM}.
