Abstract A new method is presented to develop high-order weighted essentially non-oscillatory (WENO) finite-volume schemes on structured and unstructured grids. The one-dimensional reconstruction used in the WENO-ZQ scheme is extended by introducing the concept of phantom points, which are constructed with the least-squares approximation to form a series of high-order WENO schemes. Numerical validations are performed on both regular structured grids and irregular unstructured grids. Analyses of the spectral property and numerical accuracy of the new schemes indicate attractive merits, including less dissipation and dispersion errors and low computational costs, which can be easily implemented into existing structured and unstructured grid CFD solvers.

中文翻译：

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一种在结构化和非结构化网格上实现高阶 WENO 方案的新方法

摘要 提出了一种在结构化和非结构化网格上开发高阶加权本质非振荡（WENO）有限体积方案的新方法。WENO-ZQ方案中使用的一维重构是通过引入幻象点的概念进行扩展，用最小二乘近似构造形成一系列高阶WENO方案。对规则结构化网格和不规则非结构化网格都进行了数值验证。对新方案的光谱特性和数值精度的分析表明具有吸引力的优点，包括较少的耗散和色散误差以及较低的计算成本，这些优点可以很容易地实现到现有的结构化和非结构化网格 CFD 求解器中。