SIAM Journal on Scientific Computing, Volume 42, Issue 6, Page A3932-A3956, January 2020.
A new adaptive diffusion central numerical flux within the framework of fifth-order characteristicwise alternative WENO-Z finite-difference schemes (A-WENO) with a modified local Lax--Friedrichs (LLF) flux for the Euler equations of gas dynamics is introduced. The new numerical flux adaptively adjusts the numerical diffusion coefficient present in the LLF flux. The coefficient is estimated by a suitable Rankine--Hugoniot condition, which gives a more accurate estimation of the local speed of propagation. To ensure robustness, lower and upper bounds of the coefficient are obtained with the help of the convection-pressure splitting of the Jacobian. The proposed adaptive A-WENO scheme is tested on several one- and two-dimensional benchmarks. The obtained results demonstrate that the use of the adaptive diffusion central numerical flux enhances the resolution of contact waves and improves significantly the resolution of fine-scale structures in the smooth areas of the solution while capturing shocks and high gradients in an essentially nonoscillatory manner.

中文翻译：

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基于新的自适应扩散中心数值通量的五阶A-WENO有限差分方案

SIAM科学计算杂志，第42卷，第6期，第A3932-A3956页，2020年1月。
在气体动力学的欧拉方程中，引入了具有改进的局部Lax-Friedrichs（LLF）通量的五阶特征交替WENO-Z有限差分方案（A-WENO）框架内的新的自适应扩散中心数值通量。新的数值通量可自适应地调整LLF通量中存在的数值扩散系数。该系数是通过适当的兰金-休格尼特条件估算的，该条件可以更准确地估算局部传播速度。为了确保鲁棒性，借助于雅可比行列式的对流压力分裂获得系数的上下限。所提出的自适应A-WENO方案已在多个一维和二维基准上进行了测试。