论文标题
熵保守的高阶通量在边界存在下
Entropy conservative high-order fluxes in the presence of boundaries
论文作者
论文摘要
在本文中，我们在熵稳定的有限体积/有限差异方案的背景下提出了一种新的发展。在第一部分中，我们专注于高阶熵保守通量的构建。作者已经在[LMR2002]中已经概括了tadmor提出的二阶准确熵保守的数值通量，该通量是通过简单的中心线性组合提出的高阶（$ 2p $）。我们将此结果推广到非中心的通量组合，如果需要非周期性的边界条件，这些结果特别有利。在第二部分中，证明了这些通量和[Klein2022]的熵耗散转向的宽松定理。在数值模拟中，我们验证了所有理论发现。
In this paper, we propose a novel development in the context of entropy stable finite-volume/finite-difference schemes. In the first part, we focus on the construction of high-order entropy conservative fluxes. Already in [LMR2002], the authors have generalized the second order accurate entropy conservative numerical fluxes proposed by Tadmor to high-order ($2p$) by a simple centered linear combination. We generalize this result additionally to non-centered flux combinations which is in particular favorable if non-periodic boundary conditions are needed. In the second part, a Lax-Wendroff theorem for the combination of these fluxes and the entropy dissipation steering from [Klein2022] is proven. In numerical simulations, we verify all of our theoretical findings.
