The resolution and robustness properties of a numerical scheme are two mutually restricted aspects for the detailed simulation of complex flows. In the present paper, an improved seventh-order finite difference weighted essentially non-oscillatory scheme (WENO-PR) is developed by distributing larger weights to the less smooth stencils. To meet the optimization requirements, the high-order smoothness indicator τ is modified by some constraints and a real-number index factor p is designed under the control of a wavenumber identifier. The results show that the modifications in the proposed scheme improve self-adaptation features in the smooth and discontinuous regions, which greatly balance the numerical resolution and robustness. Compared with the existing schemes such as WENO-Z and WENO-JS, the WENO-PR is more flexible, accurate and robust. Several one- and two-dimensional numerical tests are performed to confirm the high-resolution capability and the non-oscillatory property of the proposed scheme.

中文翻译：

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一种改进的加权基本非振荡方案，具有修改的平滑度指标 τ 和自适应指数 p

数值方案的分辨率和稳健性是复杂流动详细模拟的两个相互限制的方面。在本文中，通过将较大的权重分配给不太光滑的模板，开发了一种改进的七阶有限差分加权基本非振荡方案 (WENO-PR)。为满足优化要求，对高阶平滑度指标τ进行了一些约束修改，并在波数标识符的控制下设计了实数指标因子p。结果表明，所提出方案的修改提高了平滑和不连续区域的自适应特征，极大地平衡了数值分辨率和鲁棒性。与现有的 WENO-Z 和 WENO-JS 方案相比，WENO-PR 更加灵活、准确和鲁棒。