A set of arbitrarily high-order WENO schemes for reconstructions on nonuniform grids is presented. These non-linear interpolation methods use simple smoothness indicators with a linear cost with respect to the order, making them easy to implement and computationally efficient. The theoretical analysis to verify the accuracy and the essentially non-oscillatory properties are presented together with some numerical experiments involving algebraic problems in order to validate them. Also, these general schemes are applied for the solution of conservation laws and hyperbolic systems in the context of finite volume methods.

翻译：本文提出了一组适用于非均匀网格重构的任意高阶WENO格式。这些非线性插值方法采用简单的光滑度指示器，其计算复杂度随阶数线性增长，从而易于实现且计算高效。为验证其精度和本质无振荡特性，本文给出了理论分析，并结合涉及代数问题的数值实验进行验证。此外，这些通用格式被应用于有限体积法框架下守恒律和双曲型系统的求解。