In this article, we present a novel RBF-WENO scheme improving the fifth-order WENO techniques for solving hyperbolic conservation laws. The numerical flux is implemented by incorporating radial basis function (RBF) interpolation to cell average data. To do this, the classical RBF interpolation is amended to be suitable for cell average data setting. With the aid of a locally fitting parameter in the RBF, the RBF-WENO reconstruction attains an additional one order of improvement, resulting in the sixth-order of accuracy. In addition, on the purpose of detecting small scale structures and steep gradients more accurately, we present new smoothness indicators by devising a method of generalized undivided differences with exponential vanishing moments. Several experimental results are performed to confirm the effectiveness of the proposed WENO method.

在本文中，我们提出了一种新的 RBF-WENO 方案，改进了用于求解双曲守恒定律的五阶 WENO 技术。数值通量是通过将径向基函数 (RBF) 插值结合到单元平均数据来实现的。为此，对经典的 RBF 插值进行了修改，以适用于单元平均数据设置。借助 RBF 中的局部拟合参数，RBF-WENO 重建获得了额外的一级改进，从而达到了六级精度。此外，为了更准确地检测小尺度结构和陡峭梯度，我们通过设计一种具有指数消失矩的广义不可分差分方法，提出了新的平滑度指标。进行了几个实验结果以确认所提出的 WENO 方法的有效性。