This work frames the problem of constructing non-oscillatory entropy stable fluxes as a least square optimization problem. A flux sign stability condition is defined for a pair of entropy conservative flux (F∗ ) and a non-oscillatory flux (Fs ). This novel approach paves a way to construct non-oscillatory entropy stable flux (F̂) as a simple combination of (F∗ and Fs ) which inherently optimize the numerical diffusion in the entropy stable flux (F̂) such that it reduces to the underlying non-oscillatory flux (Fs ) in the flux sign stable region. This robust approach is (i) agnostic to the choice of flux pair (F∗, Fs ), (ii) does not require the computation of costly dissipation operator and high order reconstruction of scaled entropy variable to construct the diffusion term. Various non-oscillatory entropy stable fluxes are constructed and exhaustive computational results for standard test problems are given which show that fully discrete schemes using these entropy stable fluxes do not exhibit nonphysical spurious oscillations in approximating the discontinuities compared to the non-oscillatory schemes using underlying fluxes (Fs ) only. Moreover, these entropy stable schemes maintain the formal order of accuracy of the lower order flux in the pair.

中文翻译：

---

熵稳定非振荡通量：熵保守通量与非振荡通量的优化结合

这项工作将构造非振荡熵稳定通量的问题框架化为最小二乘优化问题。为一对熵保守通量定义通量符号稳定性条件（F* ）和非振荡通量（Fs ）。这种新颖的方法为构造非振荡熵稳定通量铺平了道路（F) 作为 (F* 和Fs ）本质上优化了熵稳定通量中的数值扩散（F），使其减少到潜在的非振荡通量（Fs ）在通量符号稳定区域。这种稳健的方法 (i) 与通量对的选择无关（F*， Fs ), (ii) 不需要计算昂贵的耗散算子和缩放熵变量的高阶重构来构造扩散项。构建了各种非振荡熵稳定通量，并给出了标准测试问题的详尽计算结果，这表明与使用基础通量的非振荡方案相比，使用这些熵稳定通量的完全离散方案在近似不连续性时不会表现出非物理寄生振荡（Fs ） 仅有的。此外，这些熵稳定方案保持了对中低阶通量的准确度的形式顺序。